Old results

OLD RESULTS

10th August 2009: As you may have noticed, the stats page has not been updated since the 14th of July. The problem is due to the fact that I cannot access to the FTP server containing the daily stats.
Don't worry, nothing is lost, since ranges continue to be assigned, and all computations are logged. I apologize for the inconvenience. Greg Childers has been contacted to solve this problem.
14th June 2009: The EulerNet server has some problems.
Scott Chase found (16,10,22), forcing me to update the records. Andrea Concaro now officially holds the records on powers 31 and 32 ! (Sorry, the table is too small)
Tito Piezas published an impressive 200+ pages online book about identities: http://sites.google.com/site/tpiezas/Home.
If you want to see what I look like, here is a scan about the crosswords championship: http://cboyer.club.fr/MeyrignacChampion2008.pdf (PDF thanks to Christian Boyer).
If I have some courage, I'll write a short introduction about Equal Sums of Like Powers for Dummies, since a lot of people don't understand the small introduction.
17th May 2009: Scott Chase sent two new results : (12,4,14) and (16,10,23).
A project about computing solutions to (4,1,3) finished recently: http://euler413.narod.ru/ with the discovery of 4 new small solutions. You can get the source code here: http://robert.gerbicz.googlepages.com/
Christian Boyer created a site about Morpion Solitaire: http://www.morpionsolitaire.com/, where he keeps track of the best records.
Uwe Hollerbach confirmed that TaxiCab(6) = 24153319581254312065344 in March 2008. The current best results of TaxiCab and CabTaxi are here: http://cboyer.club.fr/Taxicab.htm
In May 2008, Uwe confirmed that CabTaxi(10) = 933528127886302221000.
In November 2006, there was an article about Nuuti's discovery of (8,4,4): http://www.maa.org/editorial/mathgames/mathgames_11_13_06.html
In June 2008, I (Jean-Charles Meyrignac) became the french champion of Mots Fléchés (swedish grids style).
If you are interested in magic squares and sums of powers, I recommend that you take a look at Christian's page: http://www.multimagie.com/English/SquaresOfCubes.htm
Peter J. Ansell maintains a page about sixth power: http://www.computer-man.demon.co.uk/
I finally updated the database.txt and dataprime.txt files !
Rolan Christofferson maintains a list of (6,1,7) solutions as a Google spreadsheet: https://spreadsheets.google.com/ccc?key=pNPrFHlUozfQnE1_mCVdZVQ

31th January 2009: Sorry for the lack of recent since the last years. The project is now in its tenth year of computation !
A big thanks to all participants, let's hope that our computations will prove to be useful in a near future.
I recently got some questions about the program, mainly to fix the problems. I'm very sorry to not react faster, mostly because I'm working on other projects now, but I don't think I can help a lot on these problems.
Without Greg Childers' constant support for all these years, the project would have stopped a long time ago.
The last years, the records didn't progress well (but I probably forgot a mail, so send me your results if you found something new).
Today, Scott Chase discovered two new results on the twelveth power: (12,2,16) and (12,5,14).
9th November 2006: Nuutti Kuosa found (8,4,4), which is a new record of the form (k,m,k-m) ! Here is his splendid discovery:

3113⁸+2012⁸+1953⁸+861⁸=2823⁸+2767⁸+2557⁸+1128⁸

8th November 2006: Robert Gerbicz found 2 new solutions for (4,1,3), using his new program. His program is 100 times faster than Daniel J. Bernstein's !!!
6th November 2006: Nuutti Kuosa sent a lot of new solutions for powers 7 and 8, but no record.
5th November 2006: Sorry for the lack of update, but I was busy with the contest site I code and also on a Flash version of my peg solitaire game. I was also very lazy.
4th November 2006: Jaroslaw Wroblewski found the following 1,3,7 multigrades:

(7,4,4) 33704+32317+14977+9803=33450+32630+14664+10057
(7,4,4) 76925+52473+50279+15187=74895+64419+27857+27693
(7,4,4) 58711+42312+38285+9544=56170+51782+24427+16473
(7,3,5) 1205011+744503+678161=1186971+921065+235693+187391+96555

2nd November 2006: Robert Gerbicz found a new solution to (4,1,3):

117112081⁴=87865617⁴+34918520⁴+106161120⁴

25th October 2006: Robert Gerbicz sent me a faster program to compute (6,2,5), in other words, it may be able to boost our current distributed project !
The source code is here: euler.c
9th October 2006: Duncan Moore found several new results on 8th power:

1056⁸+129⁸+1⁸=1017⁸+873⁸+710⁸+280⁸+170⁸+86⁸
469⁸+388⁸+314⁸+2⁸=482⁸+274⁸+210⁸+149⁸+34⁸
564⁸+139⁸+52⁸+8⁸=540⁸+476⁸+364⁸+299⁸+174⁸
908⁸+530⁸+457⁸+349⁸=850⁸+791⁸+678⁸+125⁸+46⁸

3rd October 2006: Jaroslaw Wroblewski found a 18th solution to (9,k,10-k):

2152⁹+979⁹+752⁹+514⁹=2101⁹+1793⁹+1021⁹+870⁹+750⁹+112⁹

20th September 2006: I migrated my DNS from Gandi to 1and1. It's much cheaper and provides the same service.
11th September 2006: Alexander Fischer improved the non-crossing knight tours of the 14x14 from 134 to 135, and 16x16 from 182 to 183.
3rd August 2006: Jaroslaw Wroblewski collected solutions to 3rd and 4th powers:
http://www.math.uni.wroc.pl/~jwr/eslp/tables.htm
13th March 2006: Seiji Tomita discovered several new solution to (4,1,3):

582665296⁴+260052385⁴+186668000⁴=589845921⁴
1670617271⁴+632671960⁴+50237800⁴=1679142729⁴
22495595284040⁴+7592431981391⁴+27239791692640⁴=29999857938609⁴

and the Ramanujan-type identity:

(2x²+36x-54)⁴+(2x²-36x-54)⁴+(4x²-108)⁴+(4x²+108)⁴+(3x²+81)⁴=(5x²+135)⁴

His homepage is http://www3.alpha-net.ne.jp/users/fermat/index.html
16th January 2006: Doomeva from AMDUsers team sent me several logos:

11th January 2006: Tito Piezas posted a new conjecture (and kindly dedicated it to us):
http://www.geocities.com/titus_piezas/Timeline1.htm
4th January 2006: Jaroslaw Wroblewski built a list of 40 solutions to a⁴-b⁴=c⁴-d⁴=e⁴-f⁴.
1st January 2006: Yasutoshi Kohmoto sent a nice equation for 2006:

2006⁶=3858364³+1976500³+24308³=3590596³+2662272³-25512³=3561535³+2713705³+26786³

And yes, it's the seventh birthday of our distributed project !
9th October 2005: Jaroslaw Wroblewski improved a lot of 14th powers. He owns all the 14th power line, except a (14,7,13) from Greg Childers.
7th October 2005: Andrea Concaro improved the number of terms for 100th power from 1654 to 1561 ! (100,779,782) 152*2+149*3+148*28+147*2+146*8+141*6+139*2+138*2+136*5+135*7+129*3+128*8+124*12+121*4+120*6+118*24+116+109*6+107*18+106*4+105*4+104*19+99*3+97*10+95+94*12+92*3+89*17+88*22+87*12+85*9+84*14+83*17+81*27+80*2+78*3+74*17+72*6+70*10+68*10+67*12+65*3+59*14+58*14+55*18+52*18+51*16+50*7+49*8+48*29+47*7+42*6+41*18+40*4+34*2+33*6+32*12+31*12+29*7+25*30+24*10+22*16+20*9+18*9+17*4+15*22+12+11*19+10*11+9*25+7*22+5*2+4*9+1*8=153*2+151+145*14+144*8+143*2+142*30+140*5+137*13+133*4+132*40+131*11+130*9+127*4+126*22+125*8+123*9+122*31+119*3+117+114*12+113*14+112*4+110*11+108*2+103*11+102*4+101*3+100*15+96*20+93*9+91*16+90*23+86*17+82+79+76*13+75*24+71*2+69*12+66*9+64+63*8+62*22+61*13+60*16+57*3+56*8+54*13+53*5+46*13+45*13+44*7+43*7+39*23+37*5+36*10+30*10+28*5+27*10+26*11+23*24+21*13+19*2+16*14+14+13*14+8*18+6*15+3*20+2*18 (100,752,839) 154*6+153*20+151*13+149*3+148*21+147+146*20+144*15+143*6+138*13+136*16+133*7+132*20+129*28+128*5+125*16+122*19+121*9+120*5+119*13+116*21+113*9+112*8+110*3+108*19+107*6+106*10+104+102*2+101*14+100+95*19+88*9+85*25+84*8+83*8+82*2+81*2+80*8+77*7+76*20+75*4+67*3+65*21+64*3+59+57*3+56*16+52*20+51*6+48*9+47*11+44*8+39+36*6+33*13+30*5+29+27*12+25*9+24*10+23*10+21*3+18*5+16*27+15*8+12*6+11*7+6*2+5*5+4*31+2*15+1*13=155*7+152*18+150*8+145*23+142*4+141*4+140*12+139*10+137*18+135*4+134*16+131*32+130*14+127*16+124*2+118*14+117*10+115*5+114*8+111*28+109*8+105*15+103*3+99*37+98*11+96*3+94*5+93*6+92+91*15+90*30+89*2+87*9+86*8+79*12+78*6+74*38+73*2+72+71*3+70*5+69*6+68+66*2+63+62*9+61*6+60*11+58*3+55*20+54*23+53*9+50*7+49*4+46*5+45*17+43*16+42*19+41*6+40*22+38+37*7+35*11+34*26+32*2+31*5+28*24+26*10+22*6+20*5+19*14+14*23+13*9+9*14+8*3+7*13+3*6 (100,631,1142) 156+155*3+153*3+151*7+150*8+146*24+144*16+140+138*5+137*7+132*9+127*5+123*4+121+115*2+114*16+113*2+109*7+107*23+91*21+90+89*2+87*9+82*14+80*24+79*11+76+69*5+67+66*12+58*26+56*11+55+53*16+51*8+49*7+48*19+46*5+45*22+44*8+43*8+40*24+37*26+36*3+35*7+34*12+33*5+32+30*15+28*21+27*15+25*8+23+19*2+18*4+14*24+9*10+8*17+7*18+6*3+5*25+1*14=154*7+152*19+149*12+148+145*3+143*9+142*11+141+139*9+136*7+135*4+134*13+133*19+131*5+129*21+128*6+126*12+125*8+124*14+122*3+120*27+119*10+118*3+117*8+116*5+112*12+111*22+110*19+108*6+106*17+105*47+104*39+103*5+102*15+101*6+100*20+99+98*25+97*14+96*3+95*5+94*20+93*9+92*7+88*11+86*12+85*16+84*12+83*14+81*10+78*13+77*13+75*19+74*2+73*16+72*10+71*6+70+68*19+64*7+63*6+62*11+61*32+60*19+59*11+57*14+54*9+52*13+50*23+47*36+42*3+41*13+39*11+38*7+31*22+29*14+24+22*28+21*20+20*12+17*10+16*8+15*27+13*14+12*5+11*19+10*27+4*15+3+2 (100,817,822) 161*2+159+158*21+157*7+156*12+153*14+152*5+145*3+142*6+141*16+138+136*15+134*7+131+130*2+128*2+125*21+124*5+120*14+119*5+118*5+117*6+112*9+110*16+108*23+107*5+106*3+105*38+104*22+103*11+102+100*2+97*2+96+95*51+94*3+91*19+89*2+84*19+83*5+80*5+79*14+77*24+75*6+73*17+71*22+70*5+68*5+62*6+60*10+59*15+58*13+57*2+55*4+53*11+50*3+49*10+46*12+44*12+41*2+39*5+37*11+35*12+31*4+29+28*20+26+25*11+24+20*13+19*19+16*19+12*22+11*6+10*14+9*10+7*20+6*6+5*13+1*8=160*11+155*27+154*11+151*9+150*12+149*6+148*16+147*11+146*15+143*7+140*7+139*10+137*3+135*4+133*2+132*2+129*18+127*23+126*2+123*8+122*31+121*14+116*13+115+114*13+113*20+111*5+109*8+101*5+99+98*8+93*14+92*21+90*16+88*7+87*17+86*19+85*5+82*18+81*14+78*12+76*6+74*6+72*18+69+67*5+66*6+61*19+56*14+54*4+52*20+51*2+48*11+47*17+45*12+43*8+42*10+38*11+36*6+34*18+33*24+32*9+30*17+27*7+23*8+22*17+18*14+15*11+14*30+13*3+8*4+4*7+3*11 (100,781,869) 165*25+162*27+161*5+159*8+158*10+156*13+154*2+153*16+152+151*29+149*21+148*5+147*3+140*15+139*9+136*9+135*5+134*19+133*15+130*7+129+128*6+127*7+123*3+122*7+120*12+118*11+117*8+115*4+114*13+110*16+108*4+106+105*5+103*2+102*8+101*13+100*9+99*3+96*12+95*14+93*5+91*17+90*16+82+79*22+78*11+77*6+76*3+75*4+72*10+71*7+70*10+68*2+67*6+66+65*6+64+60*6+59*2+58*20+56*12+52*29+50*6+47*10+44*9+43*5+42*8+41*3+37*14+35*9+34*15+33*8+32*7+28+22+21*8+19*9+18*4+16*9+13*14+12*20+11*3+10*11+6*7=167*2+166*5+164*19+163*13+160+157*7+155*15+150*7+146*5+145*23+144*8+143+142*21+141*2+132*26+131*12+126*3+125*14+124*12+121*24+119*18+116*7+113*6+112*31+111*7+109*17+107*8+104*7+98*36+97*19+94*21+92*7+89*13+88*2+87*15+86*12+85*15+83*16+81*23+80*3+74+69*36+63*4+62*2+61*11+57*44+55*10+54*4+53*20+51*7+49*2+48*4+46*20+45*6+40*21+39+38+36+31*9+29*7+27*12+26*18+25*5+24*15+23*5+20*7+17*2+15*12+14*13+9*2+8*7+7*3+5*4+4*6+3*6+2*2+1*36 (100,757,899) 161*15+160*24+156*18+154*2+151*4+149*4+147*15+145*18+141*8+140*3+137*12+136*7+135+133*5+131*28+130*6+126*17+124*3+122*16+121*6+119+117*2+115*25+114*15+113*9+109*5+108*20+107*13+106*4+104*2+103*7+102*11+99*10+98*4+96*9+93*6+92*9+91+90*24+89*17+87*3+83*22+79*28+77*7+75*7+74*4+70+69+68*9+67*26+65*7+64*22+63*7+61*7+58*4+56+55+53*3+52*8+50*16+49+48+45*10+44*10+37*6+35+34*2+32*17+26*17+24*10+19*17+14*13+12*7+7*12+6+5*3+4*26+1*13=162*11+159*3+158*47+157+155*5+153*3+150*6+146*2+144*5+143*3+142*7+139*16+134*2+132*6+129*6+128*5+127*10+125*9+123*18+118+116*47+111*21+110*10+101*41+100*8+97*4+95*12+94+88*7+86*9+85*10+84*4+82*12+81*8+80*18+76*5+73*3+72*2+71*33+66*30+62*7+60*4+57*24+54*10+51*18+47*15+46*10+43*21+42*11+41*18+40*11+39*7+38*12+36*8+33*27+31*5+30*10+29*8+28*14+27*22+25*5+23*11+22*7+21*27+20*13+18*6+17*10+15*12+13*14+10*31+9*7+8*16+3*17+2*10 (100,764,895) 145*3+143*14+141*2+139*9+138*2+135*9+134+131*3+130*16+127*25+123*25+121*19+119*14+114*21+113*6+112*12+111*2+108*12+106*36+103*14+102*3+98*4+95*7+94+93*16+91*23+88*2+84*16+83*3+77*16+75*3+69*32+68*11+64*12+62*13+60*6+59*2+58*6+55*2+54*16+53*4+50*25+48*17+47*9+44*15+41*15+40*4+36*24+35*17+34*9+32*11+30*10+27*14+25*32+24*2+23*7+21*5+18*2+17*18+16*28+13*21+11*4+9*9+7*4+4*11+2*8=144*9+142*11+140*27+137*18+136*18+132*29+128*11+126*2+125*13+124*5+122+120*10+118*22+117*6+116*6+115*23+110*31+109+107*3+105*15+104*5+101*30+100*10+99*3+97*22+92*24+90*29+89*31+87*19+86*11+85*3+82+81*2+80*9+79*12+78*6+76*5+74*2+73*21+72*7+67*19+65*16+63*9+61*12+57*8+56*13+52*11+51*14+49*5+46*4+45*25+43*4+39*14+38*5+37*4+33*5+31*15+29*2+28*11+26*2+22*3+20*7+19*33+15*35+14*17+12*23+10*11+8+6*24+5+3+1*28 (100,709,1004) 169*15+167*2+165*4+164*20+163*13+161*7+157*5+156*16+155*31+154*6+153*3+152*9+150*11+147*8+144*4+141*25+140*34+139*8+138*3+136*13+135*5+133*15+131*11+130*11+128*18+127*16+123*2+120*6+113*12+103*13+101*8+98*9+96*27+93*13+88*14+85*4+84*17+83+79*11+76*23+72*2+67*10+66*5+62*8+61*4+60*19+59*14+58*10+56*3+51+50*11+49*3+48*5+46*24+45*13+43*2+37*6+34*25+32*11+31+26*5+23*13+20*7+17*9+16*7+14*10+4*4+3*4=168*27+166*13+162*12+160*11+159*20+158*30+151*31+149*14+148*2+145*6+142*13+137*6+132*6+129*18+126*5+125*3+124*11+122*2+121*27+119*7+118*26+117*16+116*15+115*5+114*22+112*21+111*14+110*6+109*3+107*15+106*6+105*29+104+102*29+100*4+99*4+97*19+95*9+94*2+92*16+91+89*15+87*2+86*12+82*4+81*2+80*4+78*14+77*10+75*3+74+73+71*14+70*7+69*16+68*5+65*22+64*14+63*22+57*3+55*15+53*2+52*10+44*17+42*8+41*2+40*4+39*2+38*2+36*7+35*11+33*5+30*26+29*11+28*2+27*27+25*20+24*6+21*15+19*5+15+13*4+12*18+11*3+10*3+9*2+8*4+7*8+6*23+5*12+2*29+1*2 (100,648,1079) 162*6+160*2+157*12+156*15+155*6+152*11+149*35+148*7+146*5+145*21+141*18+136+134*6+131*13+130*4+129*10+126*11+125*11+119*16+115*17+108*8+107*2+106*2+105*10+102*14+100*4+97*8+94*2+93*3+90*31+88*3+86*16+85*2+82*19+78*2+76*10+74+71+67*15+66*24+65*6+63*10+61*10+59*9+56*5+52*3+50*17+48*19+44*2+39*14+34*10+29*14+24*9+23*2+19*14+18*6+16*6+14*13+9*10+6*28+5*20+4*10+3*2+2*5=161*9+159*10+158*11+154*19+153*37+151*13+147*6+144*5+143*10+142*13+140*15+139*16+138*41+137*35+135*11+133*22+132*26+128*13+127*13+124*30+123*28+122*9+121*16+120+118*19+117*12+116*20+114+113+112*11+111*6+110*7+109*9+104+103+101*27+99*7+98*2+96*17+95*20+91*3+89*19+87*8+84*2+83*9+81*7+80*10+79*2+75*6+73*21+72*6+70*12+69*18+68*4+64*14+62*26+60*2+58*6+57*4+55*22+54*11+53*7+51*2+49*3+46*13+45*9+43*16+42*2+41+40+38*30+37*2+36*6+35*3+33*6+32*8+31*2+30*15+28+27*5+26*10+25*23+22*5+21*27+20*31+17*6+15*13+11+10*6+8*30+7*4+1*9 (100,678,1066) 155*17+154*26+149*6+147*26+146*15+144*4+140*9+139*2+135*6+133*9+131*12+130*14+129*4+125*3+124*8+122*5+120*23+118*23+111*20+107*3+103*5+101*16+99*4+94+89*6+87*3+86*10+83*7+82*4+81*13+79*7+72*15+71*6+70*3+69*9+65*11+63*10+62*4+61*7+60*15+58*7+57*2+55*7+54*18+53*19+46*2+45*21+43*2+41*3+40*8+39*3+38*2+36*8+35*9+32*10+31*12+30*9+26*13+22*11+15*24+13*25+11*9+10*6+9*12+8*7+7*18+3+2+1*18=157*5+156*5+153*7+152*7+150*4+148*26+145*37+143*21+142*8+141*19+138*26+137*3+136*18+134*29+132*16+128*2+127*8+126*7+123*20+121*4+119*5+117*13+116*16+115*7+113*12+112*10+110*30+109*18+108*27+106*12+105*6+104*5+102*2+100+98*14+97*17+96*12+93*8+92+91*21+90*5+88*33+85*15+84*16+80+78+77*18+76*10+75*31+74*5+73*20+68*13+67*5+66*5+64+59*7+56+52*11+51*6+50*7+49*4+48*25+47*6+44*6+42*15+37*19+34+33*37+29*3+28*9+27*5+25*3+24*13+23+21+20*27+19*20+18*5+17*37+16*22+14*17+12*9+6*28+5*24+4*9
15th December 2005: Sorry for the lack of recent updates, my ISP cut my DSL access since 3 weeks. Many people have asked why the top page was not updated, and I still have problems getting the stats from Greg's server. Let's hope everything will go back to normal soon.
To thank the various teams participating to our project, I'll put logos on the top page very soon.
The first team I'd like to thank for their support is Team Ninja (thank you for your patience !):

30th November 2005: Jaroslaw Wroblewski discovered (17,5,33) and some prime solutions: (13,1,59), (14,1,91) and (15,1,99).
5th November 2005: Jaroslaw Wroblewski discovered (15,4,19).
15th September 2005: Jaroslaw Wroblewski found prime solutions to (7,1,11), (7,2,10), (7,4,6) and (10,9,9) !
11st September 2005: Sorry for the lack of recent updates, but the distributed server is now working fine again ! A small trick to advanced users: if you have trouble connecting to the server, press Ctrl-U, then change the server name from eulernet.org to euler.myip.org. This may solve your problem if the DNS is incorrect.
27th August 2005: The server is still down. I have no information about its current status, but I'll post a message here when it will be restarted.
20th August 2005: Greg Childers has a problem with his motherboard. His problem will be fixed on the 23th or 24th of August. Thank you for your patience !
10th July 2005: I'm co-organizing the new Al Zimmermann's contest if you want to compete with some of the best programmers, you should take a look at this contest !
Having recently discovered Nvu, I'm now using it to edit my site. It's free and definitively one of the best HTML Wysiwyg tool !
19th June 2005: As you may have noticed, the top producers page is not frequently updated.
It's simply because I have problems connecting to the FTP server containing the stats.
I'm also working on organizing a programming contest.
27th February 2005: A forum has been setup.
23th February 2005: Alain Maye solved the last tough peg solitaire problem.
21st February 2005: Jaroslaw Wroblewski found (12,1,19), improving over his (12,1,21) !
31st January 2005: Duncan Moore found the smallest possible CabTaxi(9): 424910390480793000 !
24th January 2005: Jaroslaw Wroblewski found a new CabTaxi(9): 825001442051661504 !
20th January 2005: Jaroslaw Wroblewski found a new multigrade (7,3,5).
11th January 2005: Jaroslaw Wroblewski found (10,1,12), and shortly after a new solution to (7,4,4) and (9,4,6).
8th January 2005: Nuutti Kuosa found a new (11,6,8).
6th January 2005: Jaroslaw Wroblewski found a new multigrade (7,4,4).
3th January 2005: This page has not been update very frequently these last months, but the results are always up to date.
Today is the sixth birthday of the project. Year 2004 saw the discoveries of (9,2,8), (11,3,11), (11,4,10), (11,7,7), (12,6,11) and various results for powers larger than 14. Jim Frye found the second solution to (5,1,4) and all these other results were found by Jaroslaw Wroblewski and Nuutti Kuosa. The distributed project found a lot of new solutions to (6,2,5), but still no (6,2,4).
4th December 2004: Jaroslaw Wroblewski found a new solution to (9,5,5).
28th November 2004: Since these last months, a lot of things happened: Jaroslaw Wroblewski found (9,2,8) and several solutions on 9th power, and Nuutti Kuosa found (11,7,7) and (11,3,11) and several other solutions on 11th power. Jaroslaw and I won a programming contest: http://www.daimi.au.dk/~pzimmer/mousetrap/fullstandings.html. I'm also writing some code for my next distributed project, but I hesitate between a crossword filler http://perso.wanadoo.fr/ledefi/ or a 18 or 19 pancakes solver http://tomas.rokicki.com/pancake/witnesses.html or a closed knight tour verification http://magictour.free.fr/
5th September 2004: The project is still running. We reached the 70,000 range, and Jwb52z noticed that every hard range takes between 400,000 and 900,000 seconds (easy ranges take only a few seconds) on a 2Ghz. Jaroslaw Wroblewski discovered (17,1,39), (20,1,61), and new solutions to (9,5,5) and (9,4,6). Using his own algorithm, Jim Frye found the SECOND solution to (5,1,4): 85359⁵ = 85282⁵ + 28969⁵ + 3183⁵ + 55⁵ 29th May 2004: After several months of other activities, here is an update of the site ! Jaroslaw Wroblewski successively discovered: (12,6,11), (15,4,23), (16,1,49), (16,2,36) and (17,1,39) ! During the same time, Lars Dausch, Vera from Ufa, Bommer, Laurent Lucas, S.I. Rodrigue, toto from Ufa, Monarcho, Laurent Lucas, sala, Fumitaka Yura, Fritz Redeker discovered new solutions to (6,2,5) ! As of today, we have accumulated a total of 122 years of computation on the problem, and still no (6,2,4) solution.
Here are other things that happened during this time:
- Bernard Helmstetter wrote a morpion solitaire solitaire solver, that he distributed to verify the optimality of the current solution after move 60 http://www.ai.univ-paris8.fr/~bh/ms/.
- George Bell found a 33 final sweep on the 9x9 solitaire, and explored the peg solitaire problem with diagonal jumps (where he found a 13 jumps solution starting at c3).
- I won a prize with George Jelliss's small contest: http://www.gpj.connectfree.co.uk/gpjm.htm
- I finished third at Al Zimmermann's Programming Contest: http://villageplayers.ch/Bitzenbeitz/Standings.php (if you are a programmer, I strongly encourage you to join this interesting -but tough- contest).
- Nuutti Kuosa would like to start a search on (8,x,y) with the Resta method. EulerNet could be much more optimized for these cases.
- Steve (PathToLght) asked if two EulerNet users could be merged. I'm really sorry, but it cannot be done easily. To avoid such a problem, please enter a team name.
- I'm still searching for a game called Brain Trainer. It's a puzzle with 50 records to break. Does somebody has this game ?
- Several people asked for more informations about the morpion solitaire, like the upper bound of 324 crosses, or the solution at 209 mentioned in Jeux & Stratégies. I'm sorry, but I have no more information.
- Some of the peg solitaire solutions of the online were lost, due a clearing of the database by the provider. Since backups are done regularly, few solutions were lost, and I cannot fix the lost ones.
- Daniel Voué was the second to solve the 8x8 french crossword (after Jonathan Perret).
- The eulernet.org server was unavailable during these months, due to the fact that its IP changed. If you have problems (like Client error) during the computation, you can manually change the server name from eulernet.org to euler.myip.org. At the next reboot, the server name will be restored automatically.
- I'm working right now on fixing some bugs in Euler2000 (mainly in the server part). A new version should be available at the end of the next week. After that, I'll work on a distributed crossword filler. It will contain a PHP server, an assembly generator and some interesting technical features. Graham Toal suggested to compute 10x10 grids with an international wordlist. It will also compute 8x12 and 10x10 french crosswords.
20th January 2004: Jaroslaw Wroblewski started this year with the discoveries of (11,5,9), (11,6,8), (11,3,12), (12,2,17), (15,3,23) and (15,2,24) ! And Nuutti Kuosa concluded this serie with (11,4,10). Karel Belský found the optimal solution of the octogon problem on the tough peg solitaire puzzles. Now only 3 problems are still open ! George Bell, using a computer search, solved the central Weigleb's solitaire in 22 moves, then all the continental solitaires in 26 moves ! The FAQ has been updated, since two people asked for more information about teams.
3rd January 2004: This page has not been updated since 2 months, and a lot of things happened since the last time.
First, this is the fifth birthday of the project. Thank you for your interest !
Second, Jaroslaw Wroblewski discovered (12,1,21) and (11,1,15), breaking one of the oldest records on this page. (11,1,16) was discovered by Luigi Morelli on the 7/20/1999 !
Third, 2003 has been a prolific year for me, with the writing of several distributed projects: Triangles (http://members.aol.com/alzimmerma/TriangleSpans.html) and MagicTour (http://magictour.free.fr). I still have two ongoing projects for 2004: non-crossing knight tours and french crosswords, which will likely be ready in the first quarter 2004.
A nice example is my discovery of the first and only 8x9 french grid:

Fourth, George P. Jelliss proposed some interesting problems with a prize for the best set of solutions: http://www.gpj.connectfree.co.uk/gpjl.htm
Fifth, Yasutoshi Kohmoto sent some nice equations for 2004:

2004³ * 1000³ = 1923840³ + 975280³ - 13360³ = 1788825³ + 1324590³ - 6465³
2004⁶ = 3959307³ + 1393389³ + 1494³ = 3848682³ + 1980119³ + 27889³
2004 * 10¹⁰ = 22625³ + 20375³ - 250³

Happy new year !

17th November 2003: My crossword program found a french 8x9 grid, and in fact it's unique ! I'll publish it soon, also I intend to start a distributed computation about 8x12 crossword grids.
3rd November 2003: Jaroslaw Wroblewski found (14,1,25) ! Al Zimmermann's programming contest has started since two weeks, and I succeeded to qualify to the second round. If you are a programmer, I recommend that you try to solve this beautiful problem, and perhaps win the 500$ in the second roung and also take a look at things that you should never do (old article but new to me).
25th October 2003: Jaroslaw Wroblewski found (15,3,24) ! Duncan Moore found TaxiCab(4,3,24), TaxiCab(4,3,25), TaxiCab(4,3,32) and TaxiCab(4,3,36).
22th October 2003: Jaroslaw Wroblewski found (15,3,25) !
18th October 2003: Jaroslaw Wroblewski found (14,2,24) !
15th October 2003: Jaroslaw Wroblewski found (14,6,16) !
13th October 2003: Jaroslaw Wroblewski found (15,3,26) !
12th October 2003: Jaroslaw Wroblewski found (14,4,20) then (14,3,22) ! About the peg solitaire game, George Bell improved my script so that it allows to play with Beasley's problems. You can check his version here. If you want to play offline, you can get Andreas Sauer's freeware program, which includes 190 levels of my version.
6th October 2003: Jaroslaw Wroblewski found (14,1,27) and (15,2,28) !
29th September 2003: Stuart Gascoigne found a new solution to (7,4,4).
28th September 2003: The freeware page has been updated.
27th September 2003: George Bell and Alain Maye solved some tough solitaire problems (only 4 remain unsolved !). They are now in the section of finished problems. John D. Beasley, the author of 'The Ins and Outs of Peg Solitaire', published an article on George Jellis site, citing my computational effort on this problem and proposing some new problems. I also added some new french crosswords.
9th September 2003: Nuutti Kuosa strikes back with a new solution to (10,6,6) !
7th September 2003: Duncan Moore found Taxicab(4,3,19), which was lower than Stuart Gascoigne expected ! He also found Taxicab(4,3,24).
5th September 2003: Jaroslaw Wroblewski discovered (15,1,28) !
2nd September 2003: Jaroslaw Wroblewski discovered (15,9,13) with his new 2Gb computer. I also added my first french page, about 8x8 crosswords. Essayez donc de remplir la grille numérotée !
27th August 2003: Jaroslaw Wroblewski just discovered the beautiful (14,9,9) ! Stuart Gascoigne sent me a page about the taxicab problem on 4th power. Alain Maye found some other optimal solutions on the peg solitaire solutions, thus reducing the number of not optimally solved problems to 10. Being unable to access the EulerNet server (it seems to be a DNS problem, since the server is still running and assigning ranges), the statistics have not been updated since 18 days :-(
20th August 2003: The EulerNet server is down since 3 days. I just added a page containing my collection of Dungeon Keeper 2 maps. Alain Maye is improving the peg solitaire solutions.
6th August 2003: Yesterday, the computation of magic knight tours has finished ! The result has been reported on MathWorld. Next project will be a search on the 12x12 board. My peg solitaire program verified Harry O. Davis results on 6x6 board: a1-a1 and c1-c1 are solvable in 16 moves, and b1-b1, b2-b2, c2-c2, c3-c3 in 15 moves.
5th August 2003: Following John Beasley's suggestions, I implemented a new algorithm to solve 6x6 solitaire boards, and found a 15 moves solution on the complimentary c2 board.
31th July 2003: Jaroslaw Wroblewski just discovered (15,10,11), equalling the record of 21 terms on 15th power !
18th July 2003: Jaroslaw Wroblewski just discovered (15,6,16) !
16th July 2003: I just discovered that my Javascript Peg Solitaire has been stolen by Puzzle-Factory. If you want to use my scripts, please keep the names of the solvers, and also drop me a mail. If you liked the film Matrix and want to have a good laugh, check this movie. If you like knight tours, take a look at George Jelliss non-intersecting page, and also to the somewhat distributed project of computing magic knight tours.
1st July 2003: Helmut Rasinger noticed that the decomposition of 15170835645 was wrong. Thanks !
22nd June 2003: The Polyhedra Programming Contest has finally been won by Pascal Zimmer, with a stalinian score ! Jaroslaw Wroblewski finished 7th, and Fumitaka Yura 8th.
18th June 2003: If you use Microsoft Word, try the Bullfighter, it's like antispam but for business plans. The distributed project progresses well, with one year of computation every week. Meanwhile, I'm working on a new small distributed project about magic knight tours. If you have a fast P4 and want to do some computations, send me a mail. On the Polyhedra Programming Contest, I was pleased to see Fumitaka Yura who is now 8th, Jaroslaw Wroblewski is 6th and Pascal Zimmer 1st. Only one week left !
25th May 2003: New uncrossing knight's tour page, with a list of current records.
21st May 2003: Stuart Gascoigne previously discovered 1801049058342701083 before February 2003. It's part of sequence A080642 of the Encyclopedia of Integer Sequences. Correction: he just explored Taxicab(6) upto 68396879196114775488.
14th May 2003: Jaroslaw Wroblewski wrote some exercices to present his algorithms on (4,2,2). You can get them here. They are very interesting if you want to understand how an efficient search can be performed ! Also, he raises an interesting open question: can you find a number that can be decomposed as a sum of two fourth powers in three different ways ? This is a problem related to the Taxicab problem.
11st May 2003: The EulerNet IP has changed yesterday, and the DNS has just been updated (thanks to Jwb52z who pointed the problem !). Duncan Moore found the smallest number which is the sum of two positive co-prime cubes in four different ways:
1801049058342701083=1216102³+136635³=1165884³+600259³=1207602³+341995³=1216500³+92227³
He added that there is no other solution below 2311049³. The previous record was a decomposition in three different ways found by P. Votja in 1983:
15170835645=517³+2468³=709³+2456³=1733³+2152³
10th May 2003: If you receive spam every day, I recommend you SpamPal, which is an excellent FREE tool to reduce your amount of unsollicited mails (multilanguage and easy to install). There is also Spamihilator, SaProxy or PopFile, but I have not tested them. If you know a good antispam tool, please let me know ! Here is a huge list of Spam filter tools.
5th May 2003: I just added a new Javascript menu facility. If you use Internet Explorer, just click on the left mouse-button once.
22nd April 2003: Jaroslaw Wroblewski found (13,5,15) !
20th April 2003: Jaroslaw Wroblewski found (13,1,21) !
15th April 2003: The morpion page has been updated with new but old solutions. Dr Mingyi Tan corrected the typo in the 5th order identities.
12th April 2003: Alain Maye achieved a perfect score of 100% on the online solitaire, but the current 6*6 can be improved to 16 jumps. I just finished second to the PHP contest ! Jaroslaw Wroblewski is always in the 2 first places of Al Zimmermann's contest, and Pascal Zimmer is not very far, this clearly demonstrates the quality of these programmers ! In two days, I'll post all the advances on the morpion solitaire problem. Jagan Reddy sent me some multigrade results some time ago. Julien Elie sent me the nice equation:
9³ + 5³ + 2³ + 9*5*2 = 952
30th March 2003: There have been some interesting advances on the morpion solitaire problem thanks to Achim Flammenkamp and Pierre Berloquin (the page will be updated in a few days, when the PHP contest will finish). Alain Maye achieved the stalinian score of 99,98% on the online solitaire, always followed by Pascal Ochem with 90,28%. Finally, Jaroslaw Wroblewski is currently the first in Al Zimmermann's contest with a score of 24,95/25 ! Also, Luigi Morelli and Hugues MacKay sent some reports on the K10 search.
24th March 2003: Achim Flammenkamp improved his upper limit to the morpion solitaire: 324 crosses (36²/4) ! He expects to reduce this bound to around 250-260 crosses.
21st March 2003: Jaroslaw Wroblewski finally got (13,4,18) ! Al Zimmermann's contest has started !
20th March 2003: Jaroslaw Wroblewski found 4 solutions to (13,4,19) ! Achim Flammenkamp proved an upper limit to the morpion solitaire: 741 crosses ! Al Zimmermann's contest will start in 2 days.
17th March 2003: Jaroslaw Wroblewski found (13,5,17) ! In the latest rankings of the solitaire online game, Alain Maye achieved a terrific 99.17%, followed by Pascal Ochem with 89.39% ! These scores can change if you find a better solution on the last boards ! Uf you are interested by security and privacy, two interesting links: the SpyBot freeware (it's much better than AdAware), and the Browser security test website, which will test your browser for security problems.
13th March 2003: Jaroslaw Wroblewski found (13,5,18).
11st March 2003: If you are interested in programming contests, you can either check this current PHP contest about a collapsing game, or wait the 22nd of March to enter Al Zimmermann's contest (perhaps the world's toughest programming contest !). If you want to test the security of your browser, click here.
10th March 2003: Jaroslaw Wroblewski found (13,2,20) and (13,5,19) !
5th March 2003: Jaroslaw Wroblewski found an impressive (13,3,18) !
4th March 2003: Jaroslaw Wroblewski found (13,2,21) ! I finished fourth at the Scrabble PHP contest.
3rd March 2003: Jaroslaw Wroblewski found (13,3,20).
28th February 2003: In the online solitaire contest, Pascal Ochem is first with 88.92%, followed by Alain Maye with 87.45% then Laurent Lucas with 79.28% ! Anonymous just passed before me (jc) with 22.03% :-(
About the EulerNet project: Laurent Evrard found a new (6,2,5) the 7th of January, then Lars Dausch the 1st of February, followed by Toto from Ufanet the 2nd of February then Thilo Rottmann the 12th of February and Laurent Lucas the same day. Congratulations to all of them !
25th February 2003: Jaroslaw Wroblewski found (17,4,33) ! Since 3 months, he is the only guy who improved the table below !
21st February 2003: Jaroslaw Wroblewski found (13,1,22) ! Hugues MacKay also reported some results on the K10 search.
16th February 2003: Michael Lau found (9,3,21) with primes !
12th February 2003: Michael Lau found (9,2,22) with primes !
11st February 2003: Jaroslaw Wroblewski found 2 solutions to (13,1,23) !
10th February 2003: Jaroslaw Wroblewski found 2 more solutions to (13,1,24).
8th February 2003: Jaroslaw Wroblewski found (13,1,24) !
7th February 2003: Jaroslaw Wroblewski just found (17,5,35) ! JW is taking over the whole table ! Also, there is an interesting competition between the first three players (Alain Maye, Laurent Lucas and Pascal Ochem) on the online solitaire (click on the Display Ranking button).
6th February 2003: Jaroslaw Wroblewski found (17,1,40), (19,1,51) and (19,4,51) in a row ! Meanwhile, Lars Dausch found the first (6,2,5) above 60,000 !
2nd February 2003: Michael Lau found (7,2,12) with prime numbers !
1st February 2003: Pascal Zimmer explored the morpion solitaire upto 20 crosses, giving 22,663,033,612 positions (the computation took 100 hours) !
30th January 2003: I compiled a list of software I use commonly. Most of them are free and highly recommended. Also, you can test my unbeatable losing tic-tac-toe, try to understand the losing strategy.
28th January 2003: The french solitaire c1 has exactly 280 solutions in 20 moves.
25th January 2003: After 3 months of computation, I just finished to compute the solutions of the french solitaire c1, and got a surprise, since it's possible in 20 moves (the previous records were 21 moves). I'm running the code to extract the solutions, so they will be available soon.
Bernd Eggen pointed that the most wanted page was not up to date, and the theorems page is not indexed. Finally, Yasutoshi Kohmoto sent some pretty equations for 2003:

2003⁴ = 2021⁴-875⁴-127⁴-23⁴-6⁴
200320032003 = 669⁴+8⁴+55⁴+13⁴
2003⁵+2¹⁰+2⁵ = 13255⁴+6086⁴+491⁴+2³²+1

23rd January 2003: Anton Gutsunaev found a bug in Euler2000 4.21b ! If you try to get more than 100 ranges (which is the maximum number of ranges that the server can assign to every user), you'll get errors when connecting to the server. A temporary version 4.21c is available for download. If you asked more than 100 ranges, here is how to proceed: download the new version, stop the old version and overwrite it with the new executable, then rerun the program and force a connection (press Ctrl-E), and set Amount of Work to Get to 0, then Enter. A connection will be done and will fix your WORKSUM.INI file properly.
20th January 2003: Jaroslaw Wroblewski found (17,3,35), (17,4,34) and (19,3,54) !
17th January 2003: Pascal Zimmer enumerated the number of positions of 'morpion solitaire' upto 19 crosses (there are 4,716,194,782 positions). His program computed this in only 22 hours !
13th January 2003: Jaroslaw Wroblewski found (17,3,38) !
12th January 2003: Jaroslaw Wroblewski found (15,5,21), then (17,3,43) then (17,2,45) and later (17,2,41) !
11st January 2003: After some problems with the EulerNet domain, everything is fixed now. Jaroslaw Wroblewski discovered (15,5,21), and you can now use my tiny search engine (based on WfSearch) to search this site.
3rd January 2003: Let's start with the bad news: the IP of eulernet.org server has changed, this means that the server will be unreachable during the time the DNS are refreshed all around the world (it may take 3 days). If you want to access the server, simply open Euler2000, type Ctrl-U, and change eulernet.org to euler.myip.org. Then force the connection with Ctrl-E. This change is without danger, since closing and restarting Euler2000 will automatically change the name back to eulernet.org again.
The good news are that it's the 4th birthday of the project ! If I remember correctly, the first to join was Luigi Morelli !
2000-2001 were marked by the terrific results of Scott I. Chase, and the discovery of Integer Relations techniques by Greg Childers, with an avalanche of new results on every powers.
2002 was marked by the terrific results of Jaroslaw Wroblewski (his first result of (5,3,3) with primes is dated 3rd January 2002 !).
Speaking about Jaroslaw Wroblewski, he just discovered (15,3,27).
My predictions for this year are the confirmation of Taxicab(6), and the first discovery of a sum of seven 7th powers equal to 0.

Happy new year !

31th December 2002: I wrote a new version of Peg Solitaire in PHP/MySQL, with automated record keeping, statistics, entirely new problems, etc... Compete online with other players ! Yesterday, Jaroslaw Wroblewski found (15,2,29) !
30th December 2002: The EulerNet server is down since one week. It will be restarted next year (only in a few hours, now !). Meanwhile, Jaroslaw Wroblewski found (14,8,12), (15,2,30) and (15,3,29) !
23rd December 2002: Jaroslaw Wroblewski discovered (15,3,31), and a few hours later (15,3,30) ! Meanwhile, Pascal Zimmer found 90,462,493 positions for the morpion solitaire with 16 crosses. My computation of the french solitaire c1 is progressing too.
20th December 2002: Jaroslaw Wroblewski discovered (15,11,11) !
18th December 2002: Jaroslaw Wroblewski just discovered another killer: (15,7,14). This is the best result on 15th power !
17th December 2002: Pascal Zimmer independently verified the number of positions of the Morpion Solitaire problem, and computed values for 14 and 15 lines (respectively 18,107,008 and 36,365,073 positions). Torbjörn Alm sent a new set of results on the K10 search: 20.58% of the search-space has been explored !
14th December 2002: Jean Palesi found new references to the Taxicab problem.
13th December 2002: Laurent Evrard discovered the largest (6,2,5) result: 59995⁶+6856⁶=57974⁶+41250⁶+39372⁶+15540⁶+9499⁶. The previous one was found by Kutendorf.
12th December 2002: Jaroslaw Wroblewski discovered (11,2,14) !
11th December 2002: Jaroslaw Wroblewski discovered (15,8,14). This is the best result on 15th power ! Torbjörn Alm sent some results on the K10 search.
8th December 2002: Stuart Gascoigne found a new upper limit for Taxicab(6): Taxicab(6) <= 24153319581254312065344, since
24153319581254312065344 = 28906206³ + 582162³ = 28894803³ + 3064173³ = 28657487³ + 8519281³ = 27093208³ + 16218068³ = 26590452³ + 17492496³ = 26224366³ + 18289922³ !
2nd December 2002: Jaroslaw Wroblewski found (12,3,15), giving him all the 12th power records except (12,7,7) !
28th November 2002: Jaroslaw Wroblewski found (12,4,15) !
27th November 2002: Jaroslaw Wroblewski found (16,2,51) !
24th November 2002: Another impressive discovery from Jaroslaw Wroblewski: (10,3,11) !
19th November 2002: Another beauty discovered by Jaroslaw Wroblewski: (10,4,9) !
18th November 2002: Michael Lau found a smaller solution to (7,2,14) with prime numbers.
11st November 2002: Michael Lau found (7,1,15) with prime numbers !
10th November 2002: Stephen Montgomery-Smith found some solutions on 26th and 31th powers !
7th November 2002: Jaroslaw Wroblewski found (9,1,10) !

917⁹=851⁹+822⁹+668⁹+625⁹+574⁹+542⁹+475⁹+179⁹+99⁹+42⁹

5th November 2002: The EulerNet server had some problems in the past week. After a reboot, it works correctly again.
2nd November 2002: Torbjörn once again improved some 31th powers !
28th October 2002: Stephen Montgomery-Smith, using Jarek's congruences and Greg's program with a network of computers found a lot of results on 26th power !
26th October 2002: Torbjörn Alm again submitted a lot of results on 31th power ! I found (14,3,26) with Jaroslaw's Congru6 program.
24th October 2002: Greg Childers and Torbjörn Alm, using Wroblewski's congruences, reduced 31th power further ! Luigi Morelli reported some work on K10, finding a new but known solution. Torbjörn Alm also reported some work on K10. Now, the K10 search has almost reached 20%. Finally, I added a Javascript page. Finally, I have finished to compute the full solutions of the french peg solitaire d2: 2376 solutions of 20 moves.
19th October 2002: Greg Childers, using his SumBKZ in conjunction with Wroblewski's results improved all 31th power !
9th October 2002: Jaroslaw Wroblewski found (13,2,24) and (13,3,24) ! The euler.myip.org address will be unreachable in 6 days. If you still use Euler2000 4.20, please update your client to 4.21b.
7th October 2002: Jaroslaw Wroblewski found (13,1,25).
2nd October 2002: Jaroslaw Wroblewski found (14,1,28).
1st October 2002: Luigi Morelli reported some work on K10.
30th September 2002: New version of Euler2000 4.21b ! Download it here. What's new: better handling of reserved ranges. Now, even if you erase your WORKTODO.INI file, they are automatically restored ! Also, due to the fact that the euler.myip.org will be deactivated starting at 15th October, Euler2000 automatically changes that to the new domain name: eulernet.org. Finally, the server has been rewritten and now simultaneous connections are possible. This only means that connection to the EulerNet server will be more reliable !
27th September 2002: Jaroslaw Wroblewski attacked 18th power and found (18,1,57), (18,2,57) and (18,3,57) in a row ! Some days ago, he also found (14,4,21).
21st September 2002: Now, the good news ! There is a new version of Euler2000 (4.20 here), with some bugfixes on the server part. All reserved ranges by Laurent Evrard's computer have been recycled thanks to this new version. If you already have a 4.19 version, you don't need to update the client ! However, if you have few computers to update, I recommend this version, since it has two interesting new features: first, it sorts the ranges before working on a range, and this will speed up the search on small ranges, second, it counts more exactly the time spent on the computation. Tomorrow another good news !
20th September 2002: Two bad news: first, Mark Dodrill had to stop the search on (6,2,5). He is the current leader with more than 20% of the project done by him ! Second, one of Laurent Evrard's computers gone crazy and reserved all ranges between 58567 and around 90000 (this is perhaps due to the bug of the 15th September). I've fixed the problem into the server part, but Greg Childers email is currently deactivated :-(
Tomorrow, two good news. Meanwhile, you can still play the peg solitaire game in Javascript with 83 problems.
19th September 2002: Jaroslaw Wroblewski found (14,5,19).
16th September 2002: Using Jaroslaw Wroblewski's program, I found (14,1,32).
15th September 2002: Two bad news in a row ! First, there is a bug into Euler2000 which affects assigned values above 58385 (the program crashes !). Kirk Pearson from Internet-based Distributed Computing Projects was the first to report it, thanks ! The new version 4.19 of Euler2000 is here. Simply stop the program and overwrite the old version with the new one. I'm sorry for the inconvenience.
Second, the myip.org service will become a paid service starting 1st October 2002, so the server euler.myip.org will become unreachable. For the moment, you can still use euler.myip.org or switch to the fixed IP address: 68.66.72.46. I'll post the new domain name here when available.
10th September 2002: Jaroslaw Wroblewski found (14,1,33) (breaking his own record set one week ago) and (15,3,33) !
9th September 2002: A Peg Solitaire game in Javascript has been added. Try to break the 53 records !
4th September 2002: Jaroslaw Wroblewski found (14,1,35) !
3rd September 2002: Torbjörn Alm improved some large exponents (62nd, 73rd and 74th powers) with the new LargeSumBKZ program.
2nd September 2002: Torbjörn Alm reported some work on K10.
28th August 2002: Stuart Gascoigne explored (5,2,2) upto 2.9*10³² and Richard Collins proposed to write a MacIntosh version.
26th August 2002: Torbjörn Alm reported some work on K10.
21st August 2002: Jaroslaw Wroblewski sent 4 new results on 16th power ! If you are tired to see popups and ads in Internet Explorer, I recommend you to install AdShield. Here is my site filters for it. To use it, simply copy it over the empty one, or import it. Feel free to send me your own filters !
19th August 2002: Laurent Lucas sent new records on 23th, 25th and 31th powers. Now, he's the co-holder of 25th power record with Greg Childers !
18th August 2002: Greg Childers and Jeramy Ross reported their work on K10, without success for the moment.
17th August 2002: Roger Frye, the discoverer (in 1998 !) of (4,1,3) sent me his new site address.
14th August 2002: Jaroslaw Wroblewski "the killer" set 3 new records on 16th power: (16,3,37), (16,4,36) and (16,6,35).
13th August 2002: I became first at the contest using a new approach requiring minimal brute-force.
11th August 2002: Laurent Lucas set 5 new records on 31th power !
9th August 2002: Bruce Mitchell kindly sent me a report of (7,2,5) since one year. Too bad this cannot be credited in the top producers page.
8th August 2002: This site has been selected by "Knot a Braid of Links" as a cool math site of the week. Thank you Kabol !
(too bad the icon is so large)
7th August 2002: Jaroslaw Wroblewski found (16,1,68) !
6th August 2002: Stuart Gascoigne extended Wroblewski's theorem to Taxicab problem.
3rd August 2002: Nuutti Kuosa just found a new (11,5,9). There is an interesting programming contest with 300$ to win here (I'm currently second). 45 solutions found on (6,2,5) have been added to the database file !
24th July 2002: Jeramy Ross kindly sent another report of K10 search, thanks !
20th July 2002: To my great surprise, Michael Lau found a smaller (5,1,7) with primes !
17th July 2002: Jaroslaw Wroblewski found (12,1,22), (12,2,18) and (12,5,15) !
14th July 2002: In an attempt to find (12,2,19), Jaroslaw Wroblewski found (12,2,22), (12,2,21) and then (12,2,20) ! The Top Producers page has changed a little bit.
13rd July 2002: Jaroslaw Wroblewski kindly sent his demonstration, you can check it here. Can you improve the current upper bound of (n,n+1,n+1) ?
8th July 2002: Jaroslaw Wroblewski just found (9,2,9) ! Soon, he'll publish a demonstration that (n,n+1,n+1) exists for every n, and he can give an order of magnitude for the smaller solution !!!
7th July 2002: Carlos Rivera proposed Fermat-Catalan and Beal's conjectures on his website. If you write a fast implementation (faster than this one), I'll be glad to add it into Euler2000.
5th July 2002: Hugues MacKay sent his last packet of computation on K10, alas with no new discovery. One week ago, Jaroslaw Wroblewski found (12,1,23), improving (12,1,24) from Scott I. Chase !
27th June 2002: Martin Schroeder reported some computation on K10. That makes 2 active searchers ! Thank you Martin !
26th June 2002: Jaroslaw Wroblewski just discovered (11,2,15) ! Torbjörn Alm is currently the only active searcher on K10. Thank you for your patience Torbj !
16th June 2002: Nuutti Kuosa sent new solutions to (7,4,4) and (10,6,6), it seems that (7,k,8-k) has been well explored below 4000 ! Jaroslaw Wroblewski and Nuutti sent a lot of new results on the 11th power, but with no new record.
You can take a look at the new Top Producers page with more statistics and a real ranking system. Recently, Mark Dodrill became the first contributor before Laurent Evrard ! Their cumulated work represent 35.96% of the total project !
A little note about what is collected in the statistics: as two exponents don't take the same time, only the spent time is collected, whatever processor/speed you could have. So even if you have slow computers, you can join the search and compete for the rating. Of course, the number of solutions found by Mark Dodrill (54) will be hard to beat.
Finally, take a look at this small flash film.
10th April 2002: A new participant called Vignobles (?) found a new solution to (6,2,5). Nuutti Kuosa found 4 more solutions to (10,6,6) using his own program ! Also, Torbjörn Alm updated his high power page after some discoveries from Laurent Lucas.
4th April 2002: As usual, a lot of solutions: Jaroslaw Wroblewski discovered a lof of solutions on powers 9, 10, 11 and 12 with his own programs, Laurent Lucas on powers 23, 24, 25, 26, 27, 29, 30, 31 and 32 with SumBKZ, Greg Childers on power 28 with SumBKZ, and the EulerNet participants found 14 new solutions to (6,2,5): Mark Dodrill found 4 new, Laurent Evrard 3, Andrew Taylor 2, Rich Brown 2, Peter Zal 1, Fumitaka Yura 1 and Western Maryland College 1. Considering that after 3 years, it is hard to find a new result, I would like to congratulate everybody for these impressive discoveries !
25th March 2002: The database file is almost updated daily ! This last week, Jaroslaw Wroblewski found 5 solutions to (10,4,10), Nuutti Kuosa found 3 new solutions to (10,6,6), Laurent Lucas found 2 new results on 28th power, and Scott I. Chase found (16,9,23). Also, the first new solution to (6,2,5) has been discovered by the team of Western Maryland College, via the EulerNet server. Congratulations to all of you !
18th March 2002: The EulerNet server has recently started assigning (6,2,5), in the hope to find (6,2,4), in 3 days, it has already reserved all values below 24,000.
Meanwhile, Jaroslaw Wroblewski and Nuutti Kuosa have done a great job on 11th power, finding (11,3,13), (11,4,11), (11,5,9) and (11,6,8)! Jaroslaw also found (12,6,12) ! Nuutti has now the record on 11th power for the minimum number of terms. Today, Torbjörn Alm just found a new solution to (9,4,6) during the search of (9,k,10-k). Congratulations Nuutti, Jaroslaw and Torbjörn !!!
25th February 2002: A newcomer called Marcin Lipinski found (18,9,35). Congratulations !
24th February 2002: Every day gives us new solutions. This week, Jaroslaw Wroblewski found (9,3,8) and (11,5,10). As usual, Nuutti reported a lot of new solutions on 7th power. The EulerNet project has almost reached 99%, so the server will start assigning (6,2,5) equations as soon as all ranges on (6,1,6) will be done. The 9th power search has reached 7%.
15th February 2002: Nuutti Kuosa found a lot of new solutions on 7th power. Jaroslaw Wroblewski found an impressive (10,5,7). Finally, the site has been re-structured. Now, all the programs are there, and all the documents are there.
1st February 2002: A new search has started, using a new program. The search is to find a solution to (9,k,10-k). You can check the progress here. If you are interested to join, mail to <euler@free.fr> (minimum configuration: 256 Mb !)
Since the last week, Nuutti Kuosa found a new solution to (7,4,4). During the beta-test of the program I found a new (9,4,6) and Torbjörn Alm found a lot of new results on 18th, 22th, 24h and 30th powers !
23rd January 2002: Just to let you know that Nuutti Kuosa found 3 new solutions to (7,4,4). The most beautiful is:
2787⁷+1951⁷+1031⁷+130⁷=2816⁷+1348⁷+1146⁷+1⁷ Just an effort, and the last term will become 0 !
21st January 2002: Although the page hasn't been updated since 2 weeks, there have been a lot of work done !
First, there is a new version of SumBKZ2 here and Jaroslaw Wroblewski proposed a new way to search (7,4,4). I generalized his idea, and a new program appeared, which is able to compute (7,4,4), (8,4,4), (9,5,5) or (10,6,6). To verify its validity, Nuutti Kuosa computed (7,4,4) upto 2000 in one day and found 4 new solutions !
Meanwhile, Frank Clowes and Torbjörn Alm found some new results on high powers with SumBKZ2, Laurent Lucas suggested a great improvement.
Finally Aloril found (9,1,11) and (15,1,32) and some prime results.
10th January 2002: A lot of results from Frank Clowes (powers 27, 29 and 30), Torbjörn Alm (power 21) and me (power 28) using the last version of SumBKZ2. This version is still changing daily, but you can already start computing on any power if you want to test ! Last second: Scott I. Chase found (16,1,70) !
8th January 2002: Scott I. Chase found (16,1,71), and Fumitaka Yura found (22,6,73), (22,8,57) and (22,9,54) using an early beta of SumBKZ2. This program should be fully operational within one week. Aloril also promised to publish his programs in one month there.
3rd January 2002: Happy new year ! Two days ago, this project had its third anniversary ! There is a new program called SumBKZ2. You can download it there, if you want to test it, please reserve a range. Today, Jaroslaw Wroblewski found (5,3,3) with primes:
6379⁵+3833⁵+2657⁵ = 6089⁵+5003⁵+1777⁵ = 11522190209024647349. Also, they have the common sum 12869. Congratulations !
30th December 2001: Aloril just found (13,1,30).
28th December 2001: Just before the end of this year, Fumitaka Yura sent 84 new results, improving almost all powers above 15. Congratulations !
25th December 2001: Merry Christmas ! Yesterday, Aloril found (19,1,75) ! Also, the EulerNet server is perfectly working (thank you Nuutti !).
19th December 2001: The EulerNet server is moving ! Greg Childers, who is the host since the beginning, has to move after his successful Ph.D. (Congratulations Greg !). Nuutti Kuosa will host the EulerNet server, so during one or two days, you'll have problems accessing the EulerNet server, there is nothing to change in the configuration. Thanks for your patience !
5th December 2001: Aloril found (13,2,29).
25th November 2001: Aloril found (17,1,52) using his own method.
20th November 2001: Surprise ! A newcomer named Aloril has found 3 new results: (13,1,32), (14,1,37) and (15,1,45) ! Congratulations !
16th November 2001: Scott I. Chase found (16,3,51).
11th November 2001: Scott I. Chase found (16,3,52).
22th October 2001: Scott I. Chase found (12,3,16) !
19th October 2001: Scott I. Chase found (12,3,17) !
16th October 2001: Scott I. Chase just found (12,3,18), breaking his own yesterday's record.
15th October 2001: Scott I. Chase just found (12,3,19) !
26th September 2001: Scott I. Chase found an impressive (16,2,53). The previous record was (16,2,77) by Fumitaka Yura. Also, I'm still progressing on fast SumBKZ.
10th September 2001: Scott I. Chase found a new result: (12,1,24), giving him almost all the records on powers 8, 10 and 12 ! Congratulations Scott !
1st September 2001: At last, an update !
Scott I. Chase found (9,1,11):
252⁹=247⁹+202⁹+167⁹+133⁹+108⁹+87⁹+74⁹+30⁹+8⁹+5⁹+1⁹
and Nuutti Kuosa found 2 new solutions to (7,4,4):
10801879444156853351936=1341⁷+1168⁷+626⁷+323⁷=1298⁷+1243⁷+496⁷+421⁷
10946368267874788731545=1403⁷+797⁷+606⁷+529⁷=1384⁷+1012⁷+744⁷+489⁷
Greg Childers is also progressing on high powers.
Meanwhile, I'm working on SumsBKZ. You can check the work in progress here.
18th June 2001: At the end of this week, we'll celebrate the first anniversary of EulerNet (thank you Greg Childers for running this server !). A team called 'Western Maryland College' is progressing very well, since it's already ranked 4th on the Top Producers page.
23rd May 2001: Torbjörn Alm found 7 new results on powers 28 and 32 (and a lot more on powers above 32, check his page). Nuutti Kuosa found a new solution to (7,4,4):
1307⁷+857⁷+618⁷+400⁷=1184⁷+1133⁷+1030⁷+423⁷
The sum is equal to 6890807721574272667868.
8th May 2001: Finally an update ! Today, mirror from Chen Shuwen's site has been updated. The search is still going strong, and we will reach 800,000 before the end of this week ! Thank you to all participants ! As usual, the Top Producers page is updated daily. Torbjörn Alm is also progressing on his high powers page. Congratulations Torbjörn !
25th March 2001: Giovanni Resta sent me an interesting article about equals sums of unlike powers. You can check his whole article at http://www.imc.pi.cnr.it/~resta/unlike.html. Here are his two best discoveries:
56575⁴+32850⁴=1460⁶+1095⁶
39⁶+66⁶+93⁶+132⁶+190⁶+225⁶ = 56755³
14th March 2001: Just a little note to say that the project is running smoothly. However, the MyIP service will soon change, so participants may encounter problems connecting to the EulerNet server. Explanations will be posted here in case of problem.
18th February 2001: Torbjörn Alm found a lot of new solutions on 28th and 29th powers.
15th February 2001: The records page and the progress page have been finally updated ! Sebastián Martín Ruiz also sent a new identity.
12th February 2001: Scott I. Chase found (16,7,27) ! Although there seems to be no update, a lot of work is done on this site. For example, check the Top Producers page with all new statistics, thanks to Greg Childers ! Also, we are now official Chen Shuwen's mirror site here. Torbjörn Alm is still progressing on high powers, all powers below 37 will come on this page in a few weeks !!! Alas, programming progress is slow due to my constant illness :-(
29th January 2001: Torbjörn Alm is now in charge of the high powers. Also, I'm adding an old program to search for |a³+b³+c³| <= 10,000 and the program will be available soon. Check this page and this page.
28th January 2001: A new page about Taxicab numbers has been added.
27th January 2001: You can measure the progress of this project by looking the 02/20/2000 index and the 08/20/2000 index ! The details page and the identities page have been updated (Kohmoto's identity has been added). Yasutoshi Kohmoto also discovered some new higher bounds for the generalized taxi cab problem.
26th January 2001: Finally, after two weeks of laziness, an update ! This time a lot of new results on various powers, by Torbjörn Alm, Scott I. Chase and Fumitaka Yura. More updates tomorrow !
11th January 2001: Today, EulerNet assigned the first value above 700,000 ! Also, Laurent Evrard just became the first of the top producers, congratulations ! Greg Childers and Scott I. Chase found some results on 14th and 16th power.
3rd January 2001: Thanks to Torjörn Alm, an old challenge has been broken: now all powers below 33 have been expressed with less than 400 terms. Today's discoveries are (14,1,39) and (14,2,34) by Greg Childers and (16,5,37) by Scott I. Chase.
1st January 2001: Happy new year !
Today is the second anniversary of this project ! All equations with power below 101 have now been found with less than 2,000 terms thanks to Greg Childers, Laurent Lucas, Fumitaka Yura and Torbjörn Alm.
28th December 2000: These last days, Scott I. Chase and Fumitaka found a lot of interesting results on 15th and 16th powers, using different methods.
With the end of this year/century, a lot of progress have been done on the equations we work on. Some new methods emerged during this year, resulting in real breakthroughs like the discovery of (6,2,5) by Giovanni Resta, (8,3,5) by Scott I. Chase and results on powers above 9 by Greg Childers, Joe Crump and Fumitaka Yura. However, there are still a lot of things to discover, for example (6,1,6) that has not yet been found. In 2001, EulerNet will start working with Greg Childers' BKZ implementation. This will surely lead to some interesting discoveries (mostly on 9th power and above). Bob Scher also wants to work again on the 7 7 problem (can seven seventh powers equal to 0 ?).
Finally, I would like to thank ALL EulerNet participants, since their common efforts finished more than 52% of the total search for (6,1,6).
Just to celebrate the end of this century, I proposed the following challenge to the high powers searchers (Fumi, Torbjörn, Greg and Laurent):
on the high power page, you can see at the bottom that the lowest number of terms for all powers below 92 is now less than 2000. Can you improve the results for power 92, 94, 95, 96, 98, 99 and 100 ?
There will be a special update for the 1st of January 2001.
16th December 2000: Results are always coming daily, databases are always updated daily. Last week best results are: (16,7,40) by Scott I. Chase and (18,3,78) and (26,1,225) by Greg Childers.Torbjörn Alm and Laurent Lucas sent a lot of new results on high powers
10th December 2000: Today, Torbjörn Alm reduced the higher lower bound to 416.You can download Yura's program here. Also, a new page containing high powers has been added.
9th December 2000: Fumitaka Yura found a new algorithmic improvement which lead to a lot of new results, while Greg Childers released a new version of his BKZ implementation. Scott I. Chase found (12,6,15) and Torbjörn Alm also sent a few new results.
4th December 2000: Scott I. Chase found (12,3,20) and (12,6,16). In the end of the table, Greg Childers and Torbjörn Alm are doing a great job !
29th November 2000: The higher lowest bound for powers upto 32 is now 476, thanks to the efforts of Greg Childers, Fumitaka Yura and Torbjörn Alm ! Also, Laurent Lucas followed by Torbjörn Alm then Greg Childers started searching above 32th power. You can download the high power database here
22th November 2000: A lot of solutions again from Fumikata Yura, Greg Childers and Torbjörn Alm. The initials FY GC and TA are trusting almost all powers above 20 in the table below !
21th November 2000: The databases have been reduced. If you want to get the whole collection, download the old database or the old prime database. A lot of new results have been found by Fumikata Yura and Greg Childers !
20th November 2000: Due to an algorithmic breakthrough from Fumikata Yura, a new batch of more than 100 solutions arrived !
19th November 2000: A lot of new results from Torbjörn Alm, Fumikata Yura (13,7,13), Greg Childers, Douglas Mc Neil and Laurent Lucas !
18th November 2000: A set of new results by Torbjörn Alm, Douglas McNeil and Greg Childers (with (30,1,1737)). If you intend to find some new results, try Greg Childers's program at http://www.pa.uky.edu/~childers/sums.html (a new version will be available soon).
Also, you can subscribe to BKZ mailing list here !
14th November 2000: Due to daily new results, only the database files and the top producers page are updated daily. The more important results from the last 4 days are: a new (7,1,7) from Maurice Blondot, and an impressive (12,7,7) from Greg Childers !
10th November 2000: Greg Childers and Tobjörn Alm independently found (32,1,1921). Fumitaka Yura and them reported a lot of results.
9th November 2000: Fumitaka Yura, Greg Childers and Torbjörn Alm sent a lot of new results !
7th November 2000: Fumitaka Yura found (25,3,172) and Greg Childers found (17,6,44), (19,7,48), (21,7,68), (25,4,94) and (26,12,98).
6th November 2000: Fumitaka Yura found (18,9,45) and (19,7,65), Scott I. Chase found (29,1,1511) and Torbjörn Alm found (28,10,445), (28,13,448), (30,10,514), (30,16,520) and (32,5,1925).
5th November 2000: Greg Childers found (32,1,2177) with BKZ ! He and Torbjörn Alm sent also some more new results.
3rd November 2000: Scott I. Chase and Greg Childers sent some new solutions. Torbjörn Alm sent a lot of new results, and Matthias Koehler found a solution to (6,2,5) above 40,000.
30th October 2000: Torbjörn Alm and Greg Childers sent a lot of new results !
28th October 2000: Torbjörn Alm found (16,11,12) and Greg Childers found (30,9,625), (32,4,1924) and (32,5,1925).
27th October 2000: Scott I. Chase found (27,1,869) and (29,1,1727). Greg Childers sent a lot of prime solutions, and a lot of them improve the current known regular results ! After a full verification, older prime results give us a lot of new solutions !!!
25th October 2000: Scott I. Chase found (29,1,1979). Greg Childers found (26,25,33) and (26,27,31). Torbjörn Alm found (20,18,19), (21,15,26), (27,28,35) and (29,34,35).
24th October 2000: Scott I. Chase found (28,1,1161), Torbjörn Alm found (17,11,21) and Greg Childers found (24,14,55) and (24,15,54).
23rd October 2000: Scott I. Chase found (28,1,1190) and (29,1,2027) while Greg Childers found (19,12,31) and (21,20,20).
22nd October 2000: Greg Childers found (14,5,27), (21,11,37), (21,14,27) and (22,12,36).
EulerNet is currently reassigning all unfinished values below 600,000. Also, all values below 499,799 have been verified !
21st October 2000: Scott I. Chase found (31,1,1880), Torbjörn Alm found (14,5,28) and (17,7,29) and Greg Childers found (15,6,21), (15,9,15), (16,11,24), (16,12,24), (18,11,29), (21,16,18), (21,17,23), (21,18,22), (22,22,22), (24,15,68), (25,11,76), (25,12,70) and (31,5,287).
Greg Childers's program is now available at http://www.pa.uky.edu/~childers/sums.html
18th October 2000: Torbjörn Alm found (26,13,70), Scott I. Chase found (29,1,2065) and Greg Childers found (19,14,27), (23,11,54) and (31,7,249).
17th October 2000: Torbjörn Alm found (20,7,39). Scott I. Chase found (29,1,2813). Greg Childers found (22,22,23), (23,22,25), (29,30,40) and (31,8,275).
16th October 2000: Greg Childers found (11,4,12), (14,6,17), (15,4,24), (17,11,22), (19,16,17), (28,33,33), (31,8,276) and (32,41,43)
15th October 2000: Greg Childers found (21,19,22), (25,9,83), (29,35,36), (31,7,279) and (32,33,51)
13th October 2000: Torbjörn Alm found (19,9,35) and (23,12,56), Greg Childers found (17,13,18), (19,17,18), (21,13,32), (23,16,33), (23,20,28), (26,29,30), (27,25,39), (30,35,37) and (31,11,242).
12th October 2000: Scott I. Chase found (12,2,23), (15,11,12), (30,1,1830) and (31,1,1906). Torbjörn Alm found (14,6,18), (20,15,36). Greg Childers found (16,12,16), (17,12,18), (17,13,19), (19,10,29), (19,13,27), (20,14,37), (21,14,33), (22,14,37), (25,13,74), (28,33,35), (29,34,39), (31,6,291) and (31,14,239).
11th October 2000: Scott I. Chase found (30,1,2171), Torbjörn Alm found (17,4,42) and Greg Childers found (20,18,20), (21,15,27), (21,21,21), (23,22,24), (25,23,32), (31,37,40) among other results !
10th October 2000: Greg Childers and Joe Crump independently found (16,13,13). Torbjörn Alm found (17,7,30), (21,11,45), (22,11,57), (22,13,59), (22,14,54), (24,13,79) and (28,28,59). Greg Childers found (18,14,16), (21,14,36), (22,16,39), (23,14,40), (24,23,28), (25,15,79), (28,35,35), (31,8,308), (31,16,235) and (32,43,44).
9th October 2000: Scott Chase found (27,50,50), Torbjörn Alm found (15,8,21), (17,7,30), (21,11,45), (22,14,54) and (24,13,79). Greg Childers found (11,6,9), (16,13,14), (17,10,21), (19,11,38), (19,12,35), (20,19,19), (21,17,25), (22,16,40), (23,17,33), (25,26,33), (26,27,33), (27,28,37), (28,15,73), (28,35,36), (29,28,47), (30,38,41), (31,9,246), (31,12,245), (31,16,236) and (32,45,47).
8th October 2000: Greg Childers found (12,8,8), (13,8,9), (15,7,20), (16,13,15), (17,8,28), (17,14,14), (18,13,30), (18,15,16), (19,11,40), (21,16,32), (24,24,31), (25,28,33), (29,38,41), (30,40,42) and (32,49,50) !
Second update: Joe Crump found (24,23,32) and Greg Childers found (14,7,15), (17,11,25), (17,13,21), (19,15,21), (20,16,36), (21,12,34), (21,15,29), (24,19,35), (24,25,29), (25,27,33), (25,29,31), (28,36,38), (30,39,42), (31,8,335), (31,15,272), (31,16,266) and (32,39,54) !
7th October 2000: Joe Crump found (26,15,83), (26,33,36) and (27,24,44). Scott I. Chase found (27,39,49), (27,44,47), (27,46,47), (27,51,51), (29,43,68), (29,44,62), (29,49,67), (29,50,55), (29,59,61) and (29,61,61).
Yesterday, Scott I. Chase and Greg Childers independently discovered (12,8,9). Scott I. Chase used an exhaustive search and Greg Childers used his LLL program !
Second update: Greg Childers found (14,7,17) and (18,12,34). Torbjörn Alm found (20,8,46) and (20,11,37). Joe Crump found (21,7,114), (25,6,131), (25,11,86), (25,12,81), (25,15,83), (25,31,31), (28,38,39), (29,35,48), (30,43,43), (31,7,355), (31,9,339), (31,11,333), (31,12,324), (31,13,320), (31,16,318) and (31,36,56). Using NTL, Greg Childers found (16,13,16), (23,16,43), (24,28,28), (25,29,33), (26,28,33), (27,32,39), (28,38,39), (29,38,47) and (31,39,43).
I have problem sending emails, so please, be patient !
6th October 2000: Scott I. Chase and Greg Childers both found (12,8,9) and Joe Crump found (13,9,9), (14,8,16), (15,11,13), (17,14,18), (20,19,21) and (28,39,42). Later, Scott I. Chase found (17,18,20), (28,37,64) and (28,53,54). Greg Childers found (16,9,25), (16,10,25), (18,6,43), (18,15,19), (19,14,32), (20,10,37), (20,14,38), (21,12,44), (21,16,35), (22,12,52), (26,34,41), (26,35,40) and (27,33,44). Joe Crump found (17,7,36), (17,12,23), (17,15,17), (17,16,17), (19,12,38), (19,13,33), (19,15,24), (19,19,19), (22,15,39), (23,11,91), (24,24,38), (27,33,44).
Everything should be more clear in a few days !
5th October 2000: Using a Pari LLL implementation, Greg Childers found (14,7,18), (15,5,23), (15,8,21), (16,10,27), (16,12,26), (17,8,34), (17,9,29), (17,12,26), (17,14,25), (18,13,31), (19,10,47), (19,11,45), (19,15,36), (20,11,43), (20,12,38), (20,14,39), (20,15,38), (21,10,62), (21,12,49), (21,15,36), (22,10,61), (22,15,42), (23,13,48), (23,15,50), (24,13,85), (28,28,59), (29,13,97) !!! You can check his sources at http://www.pa.uky.edu/~childers/sums.html
2nd October 2000: Scott Chase found (12,4,16) and (12,5,16). Greg Childers found (15,6,24), (15,7,24), (15,8,23), (16,11,25), (17,10,25), (17,16,18), (18,14,34), (19,11,49), (19,14,42), (19,16,23), (20,12,41), (20,13,38), (20,22,22), (21,13,44), (22,23,23), (23,13,56), (24,30,33)
1st October 2000: Greg Childers found (16,12,27), (19,13,45), (20,13,43), (20,16,38) and (21,16,37)
29th September 2000: Scott I. Chase found (12,4,17) and Greg Childers found (20,23,23) with LLL
28th September 2000: Scott I. Chase found (12,4,18)
27th September 2000: Scott I. Chase found (12,4,20) then (12,4,19) and Joe Crump found (13,10,10), (15,6,32), (15,9,17), (16,13,28), (17,10,35), (17,11,34), (18,16,17), (18,13,37), (18,14,36), (19,5,71), (19,8,54), (19,12,52), (19,15,41), (19,16,41), (19,18,21), (20,9,51), (20,14,48), (21,11,52), (21,14,38), (21,15,37), (21,21,22), (22,10,82), (22,15,58), (22,16,41), (23,21,30), (23,14,50), (23,16,44) and (32,49,51) !
26th September 2000: Joe Crump's return ! Following Greg Childers's idea, and with the help of a Gramm-Schmidt lattice based reduction, Joe Crump atomized all previous records above 13th power. Simply take a look at the lowest number of terms at the bottom of this page, no comment ! His best results are: (13,9,12), (14,9,10), (15,10,13), (16,14,14), (17,15,19), (18,17,18), (19,21,21), (20,23,25), (21,20,24), (22,24,26), (23,26,37), (24,32,35), (25,32,35), (26,37,39), (27,24,55), (28,44,46), (29,30,57), (30,33,65), (31,49,50) and (32,52,56).
25th September 2000: Scott I. Chase found (12,4,21), JC Meyrignac found (29,1,3740), and Greg Childers found (23,48,105), (24,89,165), (25,68,137), (26,146,150), (28,86,173), (29,77,160) and (30,154,185) !! Now he holds all records above 22 !
24th September 2000: Greg Childers found (27,79,218), (28,252,368), (28,330,388), (29,271,553), (30,385,478), (31,154,341), (31,343,419) and (32,267,369) ! Now, he holds the records of number of terms on all these powers !
23th September 2000: Scott I. Chase found (31,1,2498) and (31,837,1426) !
22th September 2000: Scott I. Chase found (32,1,4302) !
21th September 2000: Scott I. Chase found (12,3,22) and (32,1,5543). EulerNet has already assigned 25% of the space search for (6,1,6) ! Thank you all !!!
20th September 2000: Kjeld Elholm Kristensen, using a great idea, found (31,758,2538), and Greg Childers found (7,1,17) prime !
18th September 2000: Scott I. Chase found (12,3,23), (12,7,16) and (31,1,3087) !!! Also, there are some new prime results.
17th September 2000: Eric Bainville's uncrossing knight tours have been added.
15th September 2000: Scott I. Chase found (31,1,4317).
14th September 2000: Scott I. Chase found (31,1,4526) and Frank Clowes found (21,2,147). EulerNet is assigning ranges at the speed of 1 percent of the total space-search every day ! At this rhythm, all values will be explored in 2 months !!!
Other news: the prime solutions have their regular page updated daily thanks to the following contributors: Torbjörn Alm, Michal Lau, Larry Hays and Laurent Lucas.
13th September 2000: Jean-Charles Meyrignac found (5,1,7) with primes. Also Torbjörn Alm and Michael Lau found new prime solutions.
12th September 2000: Frank Clowes found (18,8,65) and (21,2,168). Torbjörn Alm, Laurent Lucas and Michael Lau found some prime solutions.
11th September 2000: Torbjörn Alm, Larry Hays and Michael Lau have collected a lot of prime solutions.
8th September 2000: The prime solutions have their own page and their own database.
7th September 2000: Scott I. Chase found (12,5,19) and Frank Clowes found (21,1,204). Also, Torbjörn Alm and Larry Hays sent new prime results.
5th September 2000: Frank Clowes found (21,3,135) and Scott I. Chase found (12,2,26), (12,3,25), (12,6,17) and (31,1,5850) ! Torbjörn Alm found a lot of prime solutions.
3rd September 2000: Frank Clowes found (21,3,149). Laurent Lucas sent prime solutions for powers below 22, and they will soon have their own page. Eric Bainville sent pretty diagrams with uncrossing knight tours. They will be available very soon too.
2nd September 2000: Frank Clowes found (21,3,155)
1st September 2000: Scott I. Chase found (8,2,7), (12,3,26), (12,8,16) and (31,1,7683) with his own programs !
Mark Dodrill found 2 new solutions to (6,1,7).
27th August 2000: Version 4.18 is available for download here. Frank Clowes found (20,3,86) !
26th August 2000: Frank Clowes found (18,7,64) !
24th August 2000: Jean-Charles Meyrignac found a new solution to (6,1,7). This week-end, EulerNet server will start assigning work on (6,1,6) instead of (6,1,7). Also, version 4.18 will be released (upgrading is not necessary).
23th August 2000: Torbjörn Alm found a beautiful (11,5,11) ! Mark Dodrill found 2 new solutions to (6,1,7).
Today, all exponents below 200,000 have been assigned ! Thanks again, Greg Childers for hosting the server !!!
Also, a mailing list is now available, but needs your feedback. To subscribe, simply send "subscribe" to euler-request@ml.free.fr
22th August 2000: Changed the Top Producers page once again. Version 4.18 will be available soon !
21th August 2000: Laurent Lucas found a new (6,1,7)
19th August 2000: Mark Dodrill found 2 new solutions to (6,1,7) ! We are approaching 200,000 with EulerNet. Soon, we will switch to (6,1,6) to speed up the computations.
17th August 2000: Greg Childers found a new (6,1,7). The new Top Producers also revealed TWO older (6,1,7) -they were both found by Laurent Lucas- !
16th August 2000: Larry Hays found (17,12,36) and Laurent Lucas found (19,3,94) and (19,6,77)
15th August 2000: Greg Childers found a new solution to (6,1,7)
14th August 2000: Crazy day ! The Top Producers page has changed slightly, Jo MacLean found (23,1,434) and (31,1,11265). Eric Bainville sent me some very interesting pictures I'll put on the site soon, and Scott Chase sent solutions to (8,1,8), (8,3,5), (10,1,13), (10,4,11) and (10,5,9) !!! In fact, he seems to have discovered independently all our results on powers below 11 ten years ago, WOW !

Now, we know that eight eighth powers can sum to zero !!!
966⁸+539⁸+81⁸-954⁸-725⁸-481⁸-310⁸-158⁸=0

11st August 2000: Kjeld Elholm Kristensen found (31,1,13147). JC Meyrignac found (20,1,160)
10th August 2000: Laurent Lucas found (13,8,14), (13,9,15), (13,10,14) and (14,11,19). JC Meyrignac found (19,3,103)
9th August 2000: Jean-Charles Meyrignac found (13,7,14) and (14,7,19)
8th August 2000: Jean-Charles Meyrignac found (13,6,15) and Kjeld Elholm Kristensen found (31,1,15063) !
7th August 2000: Jean-Charles Meyrignac found (13,5,27) and (13,6,23). Laurent Lucas found a new solution to (6,1,7)
5th August 2000: Laurent Lucas found (14,8,20) and (14,12,22), Torbjörn Alm found (22,4,145), Maurice Blondot found a new solution to (7,2,6) and Greg Childers found two new solutions to (6,1,7). Also added the names of the records holders on the lowest number of terms and changed the design of the tables a little bit.
1st August 2000: Torbjörn Alm found (17,5,58). I would like to apologize to Joe and John Michael Crump. Their records are still out of the table !
30th July 2000: Torbjörn Alm found (19,4,88) and (20,4,112), also he suggested that every new record should be marked with the initials of the discoverer. Excellent idea !
28th July 2000: Laurent Lucas found (25,4,524)
25th July 2000: Laurent Lucas found (18,6,64) and (18,9,46). Also added a FAQ if you want to join the search on (6,1,7)
24th July 2000: Jean-Charles Meyrignac found (13,3,27)
23rd July 2000: Version 4.17 is available for download here
20th July 2000: Larry Hays found (17,4,59), (17,6,53) and (18,5,80), Torbjörn Alm found (15,7,35) and Laurent Lucas found (21,2,180). Also today, all values below 30,000 have been explored for (6,2,5).
19th July 2000: Torbjörn Alm found (14,9,21) and (14,10,20) and Larry Hays found (17,6,64)
18th July 2000: Torbjörn Alm found (13,10,15) and (14,10,24)
17th July 2000: A new Top Producers page is available.
Laurent Lucas found (22,2,234) and (25,2,817) and JC Meyrignac found (22,8,214)
16th July 2000: JC Meyrignac found (22,8,260), Laurent Lucas found (13,3,30) and (18,5,81)
15th July 2000: Larry Hays found (21,5,132) and (25,7,535) and Laurent Lucas found (14,5,31), (14,6,20) and (17,4,63)
14th July 2000: Larry Hays found (18,7,82) and (21,7,162)
13th July 2000: JC Meyrignac found (12,3,27), Laurent Lucas found (16,7,75)
12th July 2000: Laurent Lucas found (14,2,35), (17,2,69), (21,2,232) and (24,2,360) !
11th July 2000: Laurent Lucas found (19,2,112)
10th July 2000: Joe Crump found (17,14,55), Laurent Lucas found (23,3,257), (23,4,243) and (25,2,835).
9th July 2000: Torbjörn Alm found (13,8,18), (13,9,16) and (21,2,237).
7th July 2000: Torbjörn Alm found (14,4,30), Luke Huitt found (16,3,76), (16,4,72), (16,5,73) and (16,6,74) !!!
Today, you can beta-test the client ! With the beta 15 in the menu User Information, in the Connection, choose your connection type and enter: euler.myip.org port 21. Then click on Enter EulerNet. You'll be assigned ranges on (6,1,7).
The server is hosted by Greg Childers.
A top producers page will be available soon.
6th July 2000: Joe Crump found (18,53,17), Torbjörn Alm found (13,2,30) and JC Meyrignac found (15,4,34).
Also, today EulerNet gave us the first results for (6,1,7): 3 new solutions ! Congratulations and thanks, Greg Childers !!!
4th July 2000: Luke Huitt found (16,8,42), Joe Crump found (18,20,58) and Larry Hays found (23,7,359)
3rd July 2000: Torbjörn Alm found (13,7,19), (13,8,19) (13,9,19) and (13,10,16), Larry Hays found (20,7,155) and (22,5,258) !
2nd July 2000: The new Euler2000 beta 15 is downloadable here. The biggest news is a morpion solitaire game. Try to break the current record !
1st July 2000: Larry Hays found (19,5,79) and Torbjörn Alm found (12,5,21)
28th June 2000: Larry Hays found (19,9,100)
27th June 2000: Larry Hays found (18,8,83), Torbjörn Alm found (13,6,31).
26th June 2000: Larry Hays found (17,7,50) !!!
25th June 2000: Larry Hays found (17,7,64), (18,4,81), (18,6,82) and (21,3,215) !
24th June 2000: Larry Hays found (18,4,81), (18,6,82) and (21,3,215)
23rd June 2000: Larry Hays found (22,2,257)
22nd June 2000: Larry Hays found (18,3,82) (18,4,82) and (20,3,159).
Peter Borwein, Petr Lisonek and Colin Percival found:
(-313)^k+(-301)^k+(-188)^k+(-100)^k+(-99)^k+99^k+100^k+188^k+301^k+313^k=(-308)^k+(-307)^k+(-180)^k+(-131)^k+(-71)^k+71^k+131^k+180^k+307^k+308^kfor k=1,2,3,4,5,6,7,8,9
(-515)^k+(-452)^k+(-366)^k+(-189)^k+(-103)^k+103^k+189^k+366^k+452^k+515^k=(-508)^k+(-471)^k+(-331)^k+(-245)^k+(-18)^k+18^k+245^k+331^k+471^k+508^k for k=1,2,3,4,5,6,7,8,9
21st June 2000: (26,1,869) by Joe McLean, (14,5,33) by JC Meyrignac and (17,3,62) by Larry Hays !
20th June 2000: First results with the new Fast feature: (14,3,33) by JC Meyrignac, (15,8,29) and (15,9,24) by Laurent Lucas
18th June 2000: The new Euler2000 beta 14 is downloadable here.
17th June 2000: Using the forthcoming beta 13, Laurent Lucas found (14,3,41), (15,3,41) and (15,6,36)
16th June 2000: Joe MacLean found (32,1,6038), Laurent Lucas found (15,5,35).
15th June 2000: Laurent Lucas found (15,11,37). An icon is now present when you bookmark this site.
12th June 2000: The Crump brothers found (17,3,71), (17,13,65) and (29,22,1181). Laurent Lucas found (15,6,44) and (15,7,41).
A new beta version of Euler2000 will be available soon !
11th June 2000: Added a database containing all results.
9th June 2000: Joe Crump found (13,4,35) and (16,12,79)
8th June 2000: Laurent Lucas found (25,1,845) !
6th June 2000: Joe Crump found (17,13,66)
4th June 2000: Oups, I forgot to mention Tommy Nolan's discovery of (10,3,12), dated 2nd February 2000.
1st June 2000: Joe Crump found (16,14,31), this is a new record in terms for 16th power !
28th May 2000: Joe Crump found (13,1,33) !!!
27th May 2000: Joe Crump found (13,4,38). The design of the site has changed a little bit.
24th May 2000: Joe Crump found (15,10,36)
22th May 2000: The Crump Brothers found (14,6,38) and (26,24,441).
20th May 2000: While beta-testing Euler2000 client/server, Nuutti Kuosa found the impressive (8,1,9): 1167⁸=1094⁸+1040⁸+560⁸+558⁸+366⁸+348⁸+284⁸+271⁸+190⁸ 18th May 2000: JC Meyrignac found (26,1,1114)
12th May 2000: Joe Crump found (15,12,28), JC Meyrignac found (26,1,1267) and Joe McLean found (27,1,1059) !
9th May 2000: Joe McLean found (27,1,1363) and (28,1,1975) and JC Meyrignac found (26,1,1345)
4th May 2000: Joe McLean found (28,1,2612).
3rd May 2000: Aleksi Niemelä found (11,4,13) and Joe McLean found (29,1,3989) with his own technique !
1st May 2000: The Crump Brothers found (15,17,26) !
22nd April 2000: The Crump Brothers found (15,12,36) and (15,15,29) and Torbjörn Alm found (28,1,3252) !
The Crump Brothers later found (14,7,27), (14,4,37) and (28,54,1705) !
16th April 2000: The Crump Brothers set a new lower bound for 21th power: (21,16,140), congratulations !
Today, the beta-test of the client/server has started !
11th April 2000: The Crump Brothers are always improving the higher powers. The client/server will be beta-testable very soon. Also, try this funny link http://sodaplay.com/constructor/index.htm
2nd April 2000: Definitely moved this page to http://euler.free.fr (so counter restarted to 0). I'll start my new job tomorrow at http://www.infogrames.fr
1st April 2000: The Crump brothers found: (25,29,551), (23,18,306), (15,9,37) and (17,12,80) !
If you live in France, I recommend you the tray utility http://perso.wanadoo.fr/yves.gregoire/intarif.htm EXCELLENT !
Also, another interesting link about how much tickets are necessary to win on the english and french lotteries: http://lottery.merseyworld.com/Wheel/
29th March 2000: The Crump Bros stroke again with (17,13,69) and (20,26,138). Wow !
Euler2000 client/server will be beta-tested very soon !
27th March 2000: (15,9,44), (20,11,172) and (23,34,333) found by the Crump brothers.
23rd March 2000: The Crump brothers -Joe and John Michael- found (17,13,73), (17,20,42), (23,13,406) and (23,19,373) and Laurent Lucas found (30,1,4033), (16,5,73) and (16,11,79).
Check Joe Crump's page: http://www.spacefire.com/numbertheory/EqualSums.htm
8th March 2000: Joe McLean indepently worked on equal sums of powers. Check his page: http://www.glasgowg43.freeserve.co.uk/sumintro.htm
Euler2000 will surely include some of his searches as soon as the client/server is ready.
27th January 2000: New home page: http://euler.free.fr !
26th January 2000: Using the newest beta 9, Nuutti Kuosa found (10,2,12) in 2 hours !
112¹⁰+99¹⁰=109¹⁰+103¹⁰+83¹⁰+79¹⁰+72¹⁰+59¹⁰+59¹⁰+52¹⁰+20¹⁰+15¹⁰+5¹⁰+5¹⁰
25th January 2000: Euler2000 beta 9 is now available, and since ALL Resta's programs are here, client/server is now the priority !
4th January 2000: Euler2000 beta 6 is currently in test and a lot of new solutions have already been found !
Check this page for more results
Also, here are two new links, the first one is my software company Quantic Dream and the second one is from a participant: http://mathonline.cjb.net (very nice name)
1th January 2000: Happy new year to everybody ! And yes, this is our first birthday ! The project started one year ago.
Thanks to you, we already found some great results, and 2000 will see more results. Thanks !
20th December 1999: Still working hard onto (8,1,10) and client/server ! (6,2,4) soon !
2nd December 1999: Sorry for the slow updates, be sure that no work is lost ! I'm working onto Euler2000.
30th November 1999: Larry Hays found a new solution to (6,2,5):
20111⁶+15059⁶=18879⁶+15680⁶+14854⁶+13812⁶+2499⁶
27th November 1999: Corrected some bugs in Euler2000 beta 2.
NEW ! (6,2,5) search has started ! A new solution to (6,2,5) has already been found by Larry Hays and Tommy Nolan !
6623⁶+323⁶ = 6615⁶+2912⁶+642⁶+434⁶+363⁶
22th November 1999: Corrected some bugs in Euler2000 beta 1.
21th November 1999: The updates are less frequent, since I'm working onto Euler2000.
You can download the beta if you want to check the differences.
(6,2,5) Resta's implementation -slightly improved- now added, new AVL algorithm very soon.
7th November 1999: Nuutti Kuosa found a new solution to (7,4,4):
1105⁷+666⁷+431⁷+314⁷=1098⁷+752⁷+536⁷+130⁷=2072756588947872048896
6th November 1999: Two recommended links:
http://pobox.com/~djb/sortedsums.html (D. J. Bernstein)
http://www.nease.net/~chin/eslp/ (Chen Shuwen)
2nd November 1999: Kevin O'Hare found (13,1,36):
990¹³=989¹³+709¹³+423¹³+305¹³+225¹³+157¹³+119¹³+98¹³+73¹³+52¹³+45¹³+37¹³*2+36¹³*2+31¹³+30¹³+28¹³+27¹³+25¹³+24¹³*4+22¹³*2+20¹³+16¹³+15¹³*2+9¹³+7¹³*2+3¹³*3
1st November 1999: Check the beautiful article of Roger E. Frye how he discovered (4,1,3) in 1988. Very instructive !
Finding 95800^4 + 217519^4 + 414560^4 = 422481^4 (on the site, courtesy of R. Frye)
24th October 1999: Return from vacation, and 4 news results ! Joe Crump found (13,5,31) and (19,8,106), Larry Hays found (17,1,71) and Frank Clowes found (14,1,40) !
3327¹³+115¹³+47¹³+32¹³+27¹³=3291¹³+2840¹³+2180¹³+1323¹³+644¹³+443¹³+303¹³+211¹³+157¹³+88¹³+65¹³+38¹³+20¹³+15¹³+14¹³+12¹³*2+10¹³*2+9¹³*2+6¹³*3+5¹³*2+4¹³*3+2¹³*2
38¹⁴=35¹⁴*2+31¹⁴*4+30¹⁴*2+29¹⁴+28¹⁴+26¹⁴*4+25¹⁴*2+22¹⁴+21¹⁴*2+20¹⁴+18¹⁴*2+17¹⁴+14¹⁴*2+13¹⁴*3+12¹⁴*2+9¹⁴+8¹⁴+4¹⁴*7+2¹⁴
30¹⁷=28¹⁷*2+26¹⁷+25¹⁷*6+22¹⁷+21¹⁷*5+20¹⁷*2+19¹⁷*8+17¹⁷*8+16¹⁷*3+15¹⁷*4+14¹⁷*5+13¹⁷*4+11¹⁷*8+7¹⁷+6¹⁷+5¹⁷+4¹⁷+3¹⁷*4+2¹⁷*5+1¹⁷
1140¹⁹+632¹⁹+154¹⁹+132¹⁹+114¹⁹+56¹⁹+50¹⁹+15¹⁹=1106¹⁹+791¹⁹+1091¹⁹+832¹⁹+486¹⁹+395¹⁹+288¹⁹+240¹⁹+200¹⁹+84¹⁹+71¹⁹+64¹⁹+45¹⁹+30¹⁹+27¹⁹+24¹⁹+21¹⁹+20¹⁹+19¹⁹+18¹⁹+13¹⁹+12¹⁹+11¹⁹*5+9¹⁹*2+7¹⁹*6+6¹⁹*3+5¹⁹*19+4¹⁹*40+3¹⁹+2¹⁹*7+1¹⁹
19th October 1999: Frank Clowes found (14,1,41)
36¹⁴=34¹⁴+33¹⁴+28¹⁴*2+27¹⁴*9+26¹⁴+25¹⁴*3+24¹⁴+22¹⁴*2+21¹⁴*2+18¹⁴*2+14¹⁴+13¹⁴*5+12¹⁴*2+10¹⁴*2+7¹⁴+6¹⁴*2+4¹⁴+3¹⁴+1¹⁴*2
14th October 1999: Torbjörn Alm found (10,1,14), and Joe Crump found (14,11,21):
120¹⁰=115¹⁰+104¹⁰+91¹⁰+80¹⁰*2+74¹⁰+63¹⁰+55¹⁰+40¹⁰+35¹⁰+33¹⁰+13¹⁰+10¹⁰+5¹⁰
1053¹⁴+885¹⁴+728¹⁴+707¹⁴+132¹⁴+97¹⁴+27¹⁴+25¹⁴+20¹⁴+16¹⁴+14¹⁴=1060¹⁴+497¹⁴+337¹⁴+246¹⁴+186¹⁴+68¹⁴+57¹⁴+45¹⁴+33¹⁴+22¹⁴+18¹⁴+9¹⁴*2+7¹⁴+4¹⁴+3¹⁴*6
10th October 1999: Joe Crump found (13,9,22):
5556¹³+366¹³+263¹³+192¹³+141¹³+33¹³+15¹³+13¹³+10¹³=5416¹³+4898¹³+4609¹³+2290¹³+1347¹³+843¹³+542¹³+96¹³+47¹³+40¹³+26¹³+22¹³+20¹³+12¹³+8¹³+6¹³*2+3¹³+2¹³*4
8th October 1999: Joe Crump found (13,10,22):
1717¹³+971¹³+579¹³+57¹³+24¹³+22¹³+16¹³+4¹³+3¹³+1¹³=1600¹³+1508¹³+1605¹³+404¹³+288¹³+193¹³+137¹³+108¹³+69¹³+46¹³+39¹³+33¹³+19¹³+14¹³+13¹³+11¹³+9¹³+8¹³+6¹³*3+2¹³
6th October 1999: Joe Crump found (18,7,85):
1317¹⁸+143¹⁸+110¹⁸+48¹⁸+42¹⁸+35¹⁸+26¹⁸=1308¹⁸+1103¹⁸+1140¹⁸+871¹⁸+651¹⁸+480¹⁸+363¹⁸+275¹⁸+214¹⁸+86¹⁸+71¹⁸+56¹⁸+28¹⁸+23¹⁸+21¹⁸+19¹⁸+18¹⁸+17¹⁸*2+14¹⁸*2+12¹⁸*3+11¹⁸*2+10¹⁸*4+9¹⁸*3+8¹⁸*3+7¹⁸*4+6¹⁸*2+5¹⁸*6+3¹⁸*12+2¹⁸*20+1¹⁸*5
3rd October 1999: Joe Crump found (13,7,28):
77¹³+74¹³+61¹³+33¹³+28¹³+26¹³+22¹³=80¹³+46¹³+39¹³+16¹³*2+13¹³+10¹³+9¹³+8¹³*3+6¹³+5¹³*3+4¹³*8+3¹³*5
2nd October 1999: Joe Crump found (13,7,30):
2179¹³+318¹³+152¹³+73¹³+59¹³+46¹³+32¹³=2147¹³+1887¹³+1618¹³+1002¹³+665¹³+461¹³+225¹³+101¹³+38¹³+25¹³+22¹³+18¹³*2+11¹³+8¹³*2+7¹³*4+5¹³*3+4¹³*3+3¹³*3+1¹³
29 September 1999: Nuutti Kuosa found a new (7,4,4) and Joe Crump found (14,9,31) and (16,25,26) among other results
1045⁷+315⁷+91⁷+73⁷=1002⁷+791⁷+765⁷+184⁷
965¹⁴+856¹⁴+823¹⁴+582¹⁴+373¹⁴+207¹⁴+159¹⁴+89¹⁴+68¹⁴=983¹⁴+277¹⁴+54¹⁴+32¹⁴+23¹⁴+15¹⁴+14¹⁴+13¹⁴+12¹⁴+10¹⁴+9¹⁴*4+6¹⁴*3+4¹⁴+3¹⁴*12+1¹⁴
6077¹⁶+2560¹⁶+1690¹⁶+852¹⁶+449¹⁶+341¹⁶+203¹⁶+102¹⁶+36¹⁶+27¹⁶+25¹⁶+23¹⁶+18¹⁶*2+16¹⁶+13¹⁶+9¹⁶*3+7¹⁶*4+6¹⁶*2=6074¹⁶+4468¹⁶+3814¹⁶+1190¹⁶+611¹⁶+262¹⁶+155¹⁶+123¹⁶+86¹⁶+70¹⁶+60¹⁶+51¹⁶+41¹⁶+21¹⁶+3¹⁶*8+2¹⁶*3+1¹⁶
28 September 1999: Kevin O'Hare found (13,1,38):
931¹³=930¹³+669¹³+492¹³+346¹³+235¹³+147¹³+110¹³+92¹³+69¹³+61¹³+45¹³+35¹³+30¹³*2+28¹³+26¹³+24¹³*5+21¹³+20¹³*5+9¹³*4+8¹³*3+7¹³+3¹³*2+2¹³
27 September 1999: Joe Crump, using his own technique, found (13,9,29) and Kevin O'Hare, using Sum99, found (13,1,40)
(13,1,40): 738¹³=737¹³+540¹³+388¹³+284¹³+219¹³+171¹³+138¹³+112¹³+85¹³+73¹³+62¹³+52¹³+41¹³+37¹³+35¹³+34¹³*2+33¹³*3+30¹³+29¹³+26¹³*2+24¹³*3+22¹³+21¹³+17¹³+15¹³+13¹³+12¹³+11¹³+8¹³+7¹³+6¹³*2+3¹³*2
(13,9,29): 39017¹³+1276¹³+307¹³+145¹³+111¹³+86¹³+62¹³+39¹³+17¹³=39015¹³+22228¹³+12216¹³+6580¹³+3833¹³+2027¹³+756¹³+434¹³+221¹³+25¹³+23¹³+12¹³+11¹³*2+10¹³+9¹³+7¹³*2+6¹³+5¹³*3+4¹³*5+2¹³*2
24 September 1999: Joe Crump using his own technique of 'probabilistic' AVL found:
(13,6,35): 6683+177+137+107+67+33=6673+4928+3496+2155+1305+864+522+345+250+85+46+27+24+22+18+15+12*2+8+7+5+4+3*8+2*2+1*3
(13,9,35): 6767+5088+3878+1886+189+47+32+26+19=6780+1058+693+472+252+144+95+75+39+11*2+9+8+7*5+6+5*3+4*6+3*2+2*4+1
(14,13,36):
3269+1319+835+249+192+142+115+72+53+18+12*2+11=3261+2558+2050+528+332+92+40+31+24+22+16+7*4+6*2+5*9+4*5+2*5
(15,12,43):
215+180+190+151+59+47+37+29+25+22+21+17=218+117+97+74+19+11+10+9*3+7*5+6*3+5*7+4*5+3+2*3+1*9
20 September 1999: Nuutti Kuosa found (11,7,9)
48¹¹+28¹¹+20¹¹+15¹¹*2+14¹¹+1¹¹=44¹¹+43¹¹+42¹¹+36¹¹*2+30¹¹+22¹¹+17¹¹+3¹¹
18 September 1999: Some news about the project:
- Euler2000 will be the next version of Sum99.
- Bob Scher, Randy Ekl and JC Meyrignac are currently working onto the 7 7 search program.
- Euler2000 will include Giovanni Resta's search program for (6,2,4), and perhaps a new one for (6,1,6).
Nuutti Kuosa using a P3-450 with 768 Mb found the smallest (10,7,7) with distinct integers solution:
51¹⁰+46¹⁰+42¹⁰+24¹⁰+12¹⁰+3¹⁰+1¹⁰=52¹⁰+45¹⁰+16¹⁰+7¹⁰+6¹⁰+5¹⁰+4¹⁰=178606834730456051
12 September 1999: Nuutti Kuosa found (11,3,14):
72¹¹+56¹¹+12¹¹=69¹¹+66¹¹+53¹¹+49¹¹+43¹¹+34¹¹*2+20¹¹+9¹¹*2+8¹¹+4¹¹*2+2¹¹
10 September 1999: Chen Shuwen independently discovered a solution to (k=1,3,7):
   [184,443,556,698] = [230,353,625,673]
which has also been discovered by Nuutti Kuosa two days ago.
For more informations, check http://member.netease.com/~chin/eslp/k137.htm
8 September 1999: Chen Shuwen discovered that the new solution of (10,6,6) found by Nuutti Kuosa is also a solution to (k=2,4,6,8,10) and gives a solution to the (k=1,2,3,4,5,6,7,8,9,10,11) case of Tarry's problem.
Here is his solution:
    [ 0, 11, 24, 65, 90, 129, 173, 212, 237, 278, 291, 302 ] = [ 3, 5, 30, 57, 104, 116, 186, 198, 245, 272, 297, 299 ]
0^k+11^k+24^k+65^k+90^k+129^k+173^k+212^k+237^k+278^k+291^k+302^k=3^k+5^k+30^k+57^k+104^k+116^k+186^k+198^k+245^k+272^k+297^k+299^k
(with k=1,2,3,4,5,6,7,8,9,10,11)
For more informations, check his web site at http://member.netease.com/~chin/eslp/k1to11.htm
5 September 1999: Nuutti Kuosa found 3 new solutions to (7,4,4):
554⁷+412⁷+365⁷+146⁷=536⁷+439⁷+437⁷+65⁷
591⁷+315⁷+299⁷+97⁷=553⁷+517⁷+208⁷+66⁷
639⁷+328⁷+281⁷+175⁷=581⁷+555⁷+471⁷+320⁷
3 September 1999: Nuutti Kuosa discovered a new solution to (10,6,6):
151¹⁰+140¹⁰+127¹⁰+86¹⁰+61¹⁰+22¹⁰=148¹⁰+146¹⁰+121¹⁰+94¹⁰+47¹⁰+35¹⁰
31 August 1999: Nuutti Kuosa discovered (11,5,13), (11,6,10) and (11,7,11) !
52¹¹+30¹¹+26¹¹+24¹¹+16¹¹=50¹¹+47¹¹+36¹¹+33¹¹+25¹¹+20¹¹+18¹¹+12¹¹+11¹¹+8¹¹*2+7¹¹+5¹¹
46¹¹+39¹¹+37¹¹+22¹¹+4¹¹*2=43¹¹*2+41¹¹+31¹¹+28¹¹+26¹¹+23¹¹+18¹¹+16¹¹+15¹¹
36¹¹+20¹¹+17¹¹+10¹¹*4=34¹¹+32¹¹+31¹¹+19¹¹*2+13¹¹+11¹¹+5¹¹*4
19 August 1999: Nuutti Kuosa discovered (11,5,14):
46¹¹+37¹¹+35¹¹+17¹¹+1¹¹=42¹¹+40¹¹+39¹¹*3+33¹¹*2+31¹¹+28¹¹+24¹¹+20¹¹+19¹¹+9¹¹+4¹¹
12 August 1999: Nuutti Kuosa discovered two solutions to (12,9,9)
43¹²+33¹²+31¹²+23¹²+20¹²+16¹²*2+12¹²+6¹²=41¹²+40¹²+32¹²+30¹²*3+29¹²+5¹²*2
43¹²+34¹²+28¹²+23¹²+15¹²*3+2¹²*2=40¹²*2+37¹²+33¹²+31¹²+21¹²+16¹²+6¹²+5¹²
9 August 1999: Nuutti Kuosa discovered (11,8,8)
67¹¹+52¹¹+51¹¹*2+39¹¹+38¹¹+35¹¹+27¹¹=66¹¹+60¹¹+47¹¹+36¹¹+32¹¹+30¹¹+16¹¹+7¹¹
27 July 1999: Luigi Morelli discovered (11,2,16):
69¹¹+5¹¹=61¹¹+60¹¹+59¹¹*2+55¹¹*2+42¹¹+33¹¹*2+23¹¹+19¹¹+11¹¹+10¹¹+9¹¹+6¹¹+1¹¹
20 July 1999: Luigi Morelli discovered (11,1,16) and (11,2,17):
78¹¹=71¹¹+69¹¹+66¹¹+64¹¹+63¹¹+52¹¹+47¹¹+43¹¹+29¹¹+23¹¹*2+22¹¹+14¹¹+12¹¹+7¹¹+1¹¹
64¹¹+16¹¹=62¹¹+54¹¹+48¹¹+47¹¹*2+46¹¹+37¹¹+36¹¹+31¹¹+30¹¹+22¹¹+19¹¹+17¹¹+13¹¹*2+10¹¹*2
14 July 1999: Kevin O'Hare discovered (14,14,14):
25¹⁴+20¹⁴*4+19¹⁴*2+18¹⁴*2+12¹⁴+9¹⁴+8¹⁴*2+1¹⁴=24¹⁴+22¹⁴*4+16¹⁴*2+15¹⁴*3+11¹⁴*2+2¹⁴*2
6 June 1999: Nuutti Kuosa discovered (13,11,11):
31¹³+27¹³+23¹³*2+21¹³+19¹³+10¹³*3+6¹³*2=29¹³*2+28¹³+25¹³+24¹³+22¹³+15¹³+5¹³*2+3¹³+1¹³
25 May 1999: Nuutti Kuosa discovered (12,9,10):
38¹²+32¹²+31¹²+28¹²+22¹²+15¹²+12¹²+3¹²+2¹²=36¹²*2+33¹²+26¹²+21¹²+20¹²+10¹²+8¹²*2+7¹²
12 May 1999: Michael Lau discovered the third primitive solution to (7,4,4):
    354⁷+112⁷+52⁷+19⁷=343⁷+281⁷+46⁷+35⁷
10 May 1999: Nuutti Kuosa discovered (11,9,9):
41¹¹+37¹¹+31¹¹+24¹¹+20¹¹+14¹¹+10¹¹+3¹¹+1¹¹=40¹¹+39¹¹+30¹¹+21¹¹+21¹¹+18¹¹+6¹¹+4¹¹+2¹¹
April 1999: Giovanni Resta independently discovered (Giovanni Resta's article in PostScript format)
    1117⁶+770⁶=1092⁶+861⁶+602⁶+212⁶+84⁶
    2041⁶+691⁶=1893⁶+1468⁶+1407⁶+1302⁶+1246⁶
    2441⁶+752⁶=2184⁶+2096⁶+1484⁶+1266⁶+1239⁶
    2827⁶+151⁶=2653⁶+2296⁶+1488⁶+1281⁶+390⁶
    2959⁶+2470⁶=2954⁶+2481⁶+850⁶+798⁶+420⁶
20 April 1999: Edward Brisse discovered 1117⁶+770⁶=1092⁶+861⁶+602⁶+212⁶+84⁶
6 April 1999: Nuutti Kuosa discovered 235⁸=226⁸+184⁸+171⁸+152⁸+142⁸+66⁸+58⁸+34⁸+16⁸+6⁸
20 March 1999: Mark Dodrill discovered 568⁷=525⁷+439⁷+430⁷+413⁷+266⁷+258⁷+127⁷
12 March 1999: Luigi Morelli discovered 137⁹+69⁹=121⁹+116⁹*2+115⁹+89⁹+52⁹+28⁹+26⁹+14⁹+9⁹
Now, all the results are stored into the database

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