Computing Minimal Equal Sums Of Prime Like Powers

This page stores the status of the search with only prime values.
The number 1 is not prime, but is used in some of the solutions.

Most wanted solutions: (6,3,9) (6,2,8) (6,1,17) (7,4,8) (7,3,11) (7,2,12) (7,1,15)

15th September 2005: Jaroslaw Wroblewski found (7,1,11), (7,2,10), (7,4,6) and (10,9,9) !
16th February 2003: Michael Lau found (9,3,21) !
12th February 2003: Michael Lau found (9,2,22) !
2nd February 2003: Michael Lau found (7,2,12) !
18th November 2002: Michael Lau found (7,2,14).
11th November 2002: Michael Lau found (7,1,15) !
20th August 2002: Michael Lau found a new solution to (5,1,7) !
3rd January 2002: After one year of no update, Jaroslaw Wroblewski found (5,3,3) !
4th December 2000: Another huge update.
18th November 2000: As usual, a lot of new results. Torbjörn Alm found (27,51,55) !
10th November 2000: Greg Childers, Torbjörn Alm and Fumitaka Yura sent a lot of results.
9th November 2000: Greg Childers, Torbjörn Alm and Fumitaka Yura sent a lot of results !
6th November 2000: Greg Childers and Torbjörn Alm sent a lot of results (as usual ;-)).
5th November 2000: Laurent Lucas found (6,2,10) and Greg Childers and Torbjörn Alm sent a lot of results !
3rd November 2000: New results from Greg Childers and Torbjörn Alm !
30th October 2000: Huge set of results from Greg Childers and Torbjörn Alm !!!
28th October 2000: Laurent Lucas and Greg Childers sent a lot of new results. Torbjörn Alm send (17,8,77)
27th October 2000: Another impressive set of results from Greg Childers ! Fixed the best result for 20th power.
25th October 2000: Torbjörn Alm found 3 new results and Greg Childers found 40 !!!
24th October 2000: Greg Childers found (15,18,21), (17,11,80), (17,23,25) and (25,46,52). Torbjörn Alm found (17,23,25), (18,14,69), (19,16,62) and (24,41,41).
22nd October 2000: Greg Childers found (16,11,69), (17,6,87), (17,7,86) and (17,12,80). Using Childers program, Torbjörn Alm found (8,2,33), (11,7,19), (17,9,84) and (25,45,53).
21st October 2000: Torbjörn Alm found (11,4,31), Greg Childers found (10,3,27), (13,8,44), (13,9,41), (13,11,23), (15,15,28), (15,16,24), (16,13,70), (18,10,66) and (32,78,79).
18th October 2000: Torbjörn Alm found (10,8,18), Greg Childers found (22,38,40) and (29,58,72).
17th October 2000: Greg Childers found (17,8,84), (19,27,29), (23,38,46), (23,39,45) and (26,53,53).
16th October 2000: Greg Childers found a lot of new results.
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 and Greg Childers reported a lot of new results.
11th October 2000: Torbjörn Alm found (14,9,49) and (15,14,32). Greg Childers found (18,23,23), (19,27,31), (23,42,43), (24,45,45), (25,46,54), (26,45,63), (27,58,61), (28,65,65), (29,50,93), (30,74,74), (31,76,92), (32,85,85) among other results !
10th October 2000: Greg Childers found (7,3,12), (9,5,17), (10,10,10), (11,11,13), (11,12,13), (12,8,44), (12,12,12), (13,9,45), (13,11,41), (13,14,16), (14,10,34), (14,12,20), (14,14,22), (14,15,23), (14,16,24), (15,16,30), (15,19,21), (16,7,74), (16,8,74), (16,9,75), (16,10,76), (16,12,69), (16,14,71), (17,6,94), (17,11,91), (17,12,86), (17,13,78), (18,11,67), (18,14,70), (18,25,25), (19,30,32), (20,30,30), (21,32,36). Laurent Lucas found (23,73,77), (24,119,119), (25,84,94), (26,96,99), (27,80,105), (28,126,126), (29,97,137), (30,139,139), (31,118,164), (32,144,144).
9th October 2000: Greg Childers found (9,6,12), (12,8,44), (13,9,45), (13,14,18), (14,17,17), (15,11,46), (15,14,34), (15,19,23), (16,6,73), (16,8,75), (16,9,75), (16,12,77), (16,20,20), (17,8,111), (17,9,99), (17,12,101), (17,14,95), (17,15,78), (17,21,28), (20,31,31), (21,34,42), (22,29,53) and (22,41,41)
8th October 2000: Torbjörn Alm found (9,4,18), (11,6,26) and (14,13,36). Greg Childers found (9,6,14), (10,73,1), (11,8,22), (11,9,17), (11,10,16), (11,12,14), (11,13,13), (12,9,45), (12,10,46), (12,11,47), (12,12,48), (13,11,49), (13,12,35), (13,15,17), (13,16,16), (14,15,24), (14,16,25), (15,12,38), (15,13,37), (15,15,30), (15,17,26), (16,11,77), (16,13,78), (16,15,72), (16,16,73), (17,12,112), (17,13,98), (17,14,98), (17,16,88), (17,21,31), (18,15,71), (18,16,72), (18,26,26), (19,22,42), (20,34,34), (21,32,49) and (22,41,43).
7th October 2000: Greg Childers found (11,10,20), (12,13,13), (14,10,35) and (20,38,38).
6th October 2000: Torbjörn Alm found (22,215,289), Laurent Lucas found (18,2,445), (19,2,840) (20,2,1208) and (21,2,2533). Greg Childers found (9,7,9), (10,8,32), (10,9,17), (11,11,15), (14,15,38), (14,16,30), (15,16,34), (19,31,41), (22,52,60).
5th October 2000: Greg Childers found (8,7,7), (9,4,18), (9,7,15), (10,10,18), (11,6,38), (11,7,22), (11,8,23), (11,9,23), (11,12,16), (13,14,20), (14,11,35), (14,12,36), (14,13,37), (14,14,37), (14,16,32), (15,11,60), (15,12,48), (15,13,45), (15,14,44), (15,15,35), (17,25,29), (18,16,73), (19,17,107), (19,32,40)
2nd October 2000: Laurent Lucas found (22,2,4234), (22,3,3716) and (22,4,1488).
Greg Childers found (11,9,31), (11,10,21), (11,11,18), (11,12,18), (11,14,15), (14,14,38), (14,16,40) and (15,16,48).
1st October 2000: Greg Childers found (9,6,16), (11,10,26) and (11,12,22)
29th September 2000: Torbjörn Alm found (11,3,47) and Laurent Lucas found (12,6,58), (15,1,235), (18,1,632), (20,1,2462) and (22,1,5460)
27th September 2000: Larry Hays found (17,1,477). Michael Lau found (16,1,412) and (20,1,2939).
Laurent Lucas found (16,1,411) and (19,1,1093). Torbjörn Alm found (11,5,44) and Joe Crump found (8,8,8), (9,8,8), (10,11,11), (11,13,15), (12,14,14), (13,13,23), (13,15,21), (13,16,18), (14,19,19), (15,17,29), (16,22,22), (17,27,31), (18,30,30), (19,30,46), (20,39,39) and (21,45,49).
26th September 2000: Larry Hays found (18,1,933) and (19,1,1586). Torbjörn Alm found (18,3,479) and (21,3,1395). Greg Childers found (8,12,13), (15,41,116), (17,75,94), (18,105,153), (19,79,128), (20,144,256) and (21,202,325) !
24th September 2000: Torbjörn Alm found (17,5,375) and (18,3,581)
23th September 2000: Torbjörn Alm found (7,3,13), (19,4,925) and (21,4,2470)
20th September 2000: Greg Childers found (7,1,17)
19th September 2000: Larry Hays found (13,1,96) and (15,1,264), Torbjörn Alm found (11,3,48), (17,3,405) and (17,4,404)
18th September 2000: Torbjörn Alm found (12,5,57) and (13,3,93) and Larry Hays found (13,1,114)
17th September 2000: Larry Hays found (9,5,19), (17,1,528) and (17,2,438). Torbjörn Alm found (10,2,42), (10,3,36), (10,4,28), (11,4,45), (18,2,843) and (19,2,963). Michael Lau found (13,1,120)
16th September 2000: Larry Hays found (11,2,47), (19,2,1374) and (20,2,1538), Michael Lau found (13,1,122) and (16,1,416)
15th September 2000: Torbjörn Alm found (7,2,14) and (15,2,161), Michael Lau found (12,1,79) and Larry Hays found (13,2,103).
14th September 2000: Torbjörn Alm found (7,2,16) and Michael Lau found (13,1,124) and (20,1,3097)

KNOWN LOWER BOUNDS
k\m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
2 5
(JCM)		 2
(JCM)		                            
3 3
(JCM)		 2
(JCM)		                            
4 17
(AL)		 2
(JCM)		                            
5 7
(JCM)		 6
(MLA)		 3
(JW)		                          
6 19
(JCM)		 10
(LL)		 3
(AL)		                          
7 11
(JW)		 10
(JW)		 9
(DM)		 6
(JW)		 5
(LL)		                      
8 33
(AL)		 33
(TA)		 33
(LL)		 34 35 6
(AL)		                    
9 21
(AL)		 22
(MLA)		 21
(MLA)		 14
(DM)		 13
(GC)		 8
(GC)		 9
(GC)		                  
10 36
(AL)		 26
(GC)		 27
(GC)		 28
(TA)		 27
(GC)		 28
(GC)		 21
(GC)		 18
(TA)		 9
(JW)		              
11 40
(AL)		 41 36
(FY)		 27
(GC)		 21
(TA)		 20
(TA)		 19
(TA)		 16
(GC)		 17
(GC)		 14
(GC)		 13
(GC)		 13
(GC)		        
12 65
(AL)		 66 54
(TA)		 54
(TA)		 43
(FY)		 42
(GC)		 42
(FY)		 43
(FY)		 25
(FY)		 24
(GC)		 25
(GC)		 12
(GC)		        
13 91
(AL)		 92 67
(GC)		 58
(TA)		 50
(FY)		 39
(FY)		 40
(FY)		 37
(FY)		 34
(FY)		 35
(FY)		 23
(GC)		 20
(GC)		 19
(GC)		 16
(GC)		 17
(GC)		  
14 97
(TA)		 98 87
(TA)		 52
(TA)		 53 54 40
(GC)		 41 41
(GC)		 33
(GC)		 29
(DM)		 20
(GC)		 21 22
(GC)		 23
(GC)		 16
(GC)
15 115
(TA)		 108
(TA)		 85
(TA)		 56
(TA)		 57 58 54
(GC)		 50
(GC)		 41
(GC)		 38
(GC)		 29
(GC)		 30 30
(TA)		 28
(GC)		 28
(GC)		 24
(GC)
16 139
(TA)		 139
(GC)		 138
(TA)		 71
(GC)		 71
(GC)		 71
(FY)		 72
(FY)		 72
(FY)		 73
(GC)		 74
(GC)		 69
(GC)		 69
(GC)		 70
(GC)		 71
(GC)		 71
(GC)		 72
(GC)
17 124
(TA)		 123
(TA)		 105
(FY)		 105
(GC)		 98
(FY)		 87
(GC)		 86
(GC)		 77
(TA)		 78 79 73
(DM)		 72
(GC)		 73 69
(GC)		 70 66
(TA)
18 193
(TA)		 154
(GC)		 155 140
(TA)		 140
(TA)		 119
(TA)		 87
(GC)		 65
(FY)		 65
(FY)		 66
(GC)		 66
(GC)		 67 68
(GC)		 69
(TA)		 70
(TA)		 70
(FY)
19 268
(TA)		 210
(TA)		 191
(TA)		 168
(GC)		 155
(TA)		 156 153
(GC)		 112
(GC)		 113 89
(FY)		 90 91 76
(FY)		 66
(FY)		 66
(GC)		 59
(GC)
20 276
(GC)		 277
(GC)		 258
(GC)		 180
(TA)		 181
(GC)		 182
(GC)		 183
(GC)		 184
(GC)		 185
(GC)		 165
(GC)		 143
(GC)		 144 140
(GC)		 141 141
(GC)		 95
(GC)
21 278
(TA)		 279 263
(TA)		 262
(GC)		 235
(TA)		 225
(FY)		 195
(TA)		 196 155
(GC)		 156 115
(GC)		 116 117 99
(FY)		 97
(FY)		 89
(FY)
22 425
(TA)		 402
(TA)		 284
(GC)		 285 258
(FY)		 259 191
(GC)		 192
(TA)		 177
(GC)		 178 173
(GC)		 174 174
(GC)		 153
(GC)		 154
(GC)		 130
(FY)
23 497
(TA)		 373
(FY)		 374 368
(TA)		 347
(TA)		 318
(FY)		 292
(GC)		 293 271
(GC)		 267
(GC)		 225
(GC)		 212
(GC)		 183
(TA)		 184 183
(TA)		 184
24 456
(TA)		 290
(GC)		 291
(GC)		 292 293
(GC)		 294
(GC)		 295
(GC)		 296
(GC)		 297
(GC)		 234
(GC)		 183
(TA)		 184 185 186 187 188
25 714
(TA)		 591
(GC)		 490
(TA)		 447
(TA)		 444
(GC)		 404
(GC)		 405 382
(TA)		 358
(GC)		 313
(TA)		 314 315 275
(GC)		 276 277 261
(TA)
26 749
(TA)		 639
(TA)		 573
(TA)		 555
(TA)		 482
(TA)		 454
(GC)		 455 403
(TA)		 404 405 324
(GC)		 325 325
(GC)		 326 327 280
(GC)
27 800
(TA)		 710
(GC)		 677
(GC)		 402
(TA)		 403 404 405 406 407 408 409 410 411 412 413 348
(TA)
28 828
(TA)		 704
(TA)		 705 468
(GC)		 440
(GC)		 441 442
(GC)		 443
(GC)		 444
(GC)		 445
(TA)		 446
(GC)		 447
(GC)		 448
(GC)		 449
(GC)		 450
(GC)		 435
(TA)
29 1042
(TA)		 980
(TA)		 884
(TA)		 718
(GC)		 719 710
(GC)		 681
(GC)		 569
(TA)		 570 571 572 573 574 566
(GC)		 465
(GC)		 466
30 1233
(GC)		 695
(TA)		 696
(TA)		 697
(TA)		 698 699
(GC)		 700
(GC)		 624
(GC)		 513
(TA)		 514
(TA)		 515
(TA)		 516 517
(GC)		 518
(TA)		 519
(GC)		 520
(GC)
31 1056
(TA)		 1057 949
(TA)		 950 845
(TA)		 846 768
(TA)		 769 770 771 772 773 701
(TA)		 702 703 690
(TA)
32 1581
(TA)		 1282
(GC)		 1157
(TA)		 1158 1159 1160 647
(TA)		 648 649
(GC)		 650
(GC)		 651
(GC)		 652
(GC)		 653
(GC)		 654
(GC)		 655
(GC)		 656
(GC)

LOWEST NUMBER OF TERMS
k 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
m+n 4
 4
 4
 6
(JW)		 6
(AL)		 10
(JW,LL)		 12
(AL)		 14
(GC)		 18
(JW)		 24
(GC)		 24
(GC)		 30
(GC)		 32
(GC)		 39
(GC)		 40
(GC)		 48
(GC)
k 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
m+n 46
(GC)		 56
(GC)		 58
(TA)		 68
(GC)		 78
(DM,GC)		 79
(DM)		 82
(TA)		 96
(DM)		 105
(TA)		 106
(TA)		 118
(TA)		 130
(GC)		 127
(GC)		 148
(TA)		 157
(GC)
AN: Aleksi Niemelä BS: Bob Scher DA: David Alten DM: Douglas McNeil EB: Edward Brisse
EB2: Eric Bainville FC: Frank Clowes FY: Fumitaka Yura GR: Giovanni Resta JC: Joe Crump
JCM: Jean-Charles Meyrignac JMC: John Michael Crump JML: Joe MacLean JW: Jareslaw Wroblewski KEK: Kjeld Elholm Kristensen
KO: Kevin O'Hare LHA: Larry Hays LHU: Luke Huitt LL: Laurent Lucas LM: Luigi Morelli
LP: Lander and Parkin MD: Mark Dodrill MLA: Michael Lau MW: Mac Wang NH: Norman Ho
NK: Nuutti Kuosa PG: Pascal Gelebart RE: Randy Ekl RS: Rizos Sakellariou SIC: Scott I.Chase
TA: Torbjörn Alm TN: Tommy Nolan
LOWEST NUMBER OF TERMS
k 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
m+n 4
 4
 4
 6
(JW)		 8
(JCM)		 10
(LL)		 14
(GC)		 14
(GC)		 20
(GC)		 24
(GC)		 24
(GC)		 30
(GC)		 32
(GC)		 39
(GC)		 40
(GC)		 48
(GC)
k 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
m+n 46
(GC)		 56
(GC)		 58
(TA)		 68
(GC)		 78
(DM,GC)		 79
(DM)		 82
(TA)		 96
(DM)		 105
(TA)		 106
(TA)		 118
(TA)		 130
(GC)		 127
(GC)		 148
(TA)		 157
(GC)
LEGEND
power (k)
number of left terms (m)
number of right terms (n), unexplored
number of right terms (n), known lower bound
number of right terms (n), best lower bound currently found
number of right terms (n), best lower bound conjectured
number of right terms (n), best lower bound proved
number of right terms (n) that doesn't need to be explored

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