| Computing Minimal Equal Sums Of High Like Powers |
This page stores the status of the search on powers above 32.
1st January 2001: If you want to join the search on high powers (where
you should have more success than low powers), join the internal mailing list
here to send
your results.
All best lower bounds are now less than 2,000 !
28th December 2000: If you want to join the fun on this search, first download
SumBKZ and check
at Greg Childer's page
how to use it. Download also Fumitaka Yura's ResultLC2,
a tool to combine solutions to obtain better ones !
10th December 2000: Creation of this page.
| k\m | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
| 33 | 338 (FY) |
318 (TA) |
259 (TA) |
260 | 245 (TA) |
246 | 235 (TA) |
214 (TA) |
205 (TA) |
206 | 201 (TA) |
192 (TA) |
193 | 194 | 181 (TA) |
182 |
| 34 | 358 (TA) |
346 (TA) |
344 (TA) |
342 (TA) |
291 (TA) |
292 | 290 (TA) |
291 | 288 (TA) |
270 (TA) |
271 | 255 (TA) |
246 (GC) |
247 | 215 (TA) |
216 |
| 35 | 436 (TA) |
417 (TA) |
401 (TA) |
345 (TA) |
346 | 320 (TA) |
317 (TA) |
308 (TA) |
309 | 308 (TA) |
252 (TA) |
253 | 254 | 250 (TA) |
251 | 242 (TA) |
| 36 | 492 (TA) |
450 (TA) |
377 (TA) |
378 | 379 | 373 (TA) |
374 | 346 (TA) |
342 (TA) |
342 (TA) |
322 (TA) |
314 (TA) |
309 (TA) |
310 | 311 | 281 (TA) |
| 37 | 31154 (LL) |
20820 (LL) |
20797 (LL) |
20789 (LL) |
20753 (LL) |
20737 (LL) |
20738 | 20627 (LL) |
20576 (LL) |
20577 | 20560 (LL) |
20561 | 20542 (LL) |
20543 | 20543 (LL) |
20544 |
| 38 | 3009 (TA) |
2790 (TA) |
2706 (TA) |
2684 (TA) |
2659 (TA) |
1891 (GC) |
1808 (GC) |
1741 (GC) |
1679 (GC) |
1650 (FY) |
1641 (FY) |
1642 | 1628 (GC) |
1624 (GC) |
1596 (GC) |
1595 (GC) |
| 39 | 667 (TA) |
525 (TA) |
477 (TA) |
478 | 408 (TA) |
409 | 393 (TA) |
394 | 374 (TA) |
374 (TA) |
372 (TA) |
373 | 369 (TA) |
365 (TA) |
352 (TA) |
345 (TA) |
| 40 | 852 (TA) |
551 (TA) |
499 (TA) |
500 | 459 (TA) |
460 | 458 (TA) |
458 (TA) |
458 (TA) |
425 (TA) |
426 | 427 | 421 (TA) |
422 | 422 (TA) |
423 |
| 41 | 610 (TA) |
591 (TA) |
574 (TA) |
575 | 561 (TA) |
438 (TA) |
439 | 440 | 441 | 356 (GC) |
357 | 358 | 359 | 312 (TA) |
309 (TA) |
310 |
| 42 | 917 (TA) |
825 (TA) |
669 (TA) |
670 | 671 | 644 (TA) |
613 (TA) |
614 | 539 (TA) |
540 | 541 | 542 | 543 | 544 | 542 (TA) |
538 (TA) |
| 43 | 913 (TA) |
778 (TA) |
770 (TA) |
688 (TA) |
689 | 657 (TA) |
622 (TA) |
608 (TA) |
596 (TA) |
597 | 591 (TA) |
578 (TA) |
557 (TA) |
552 (TA) |
539 (TA) |
531 (TA) |
| 44 | 809 (TA) |
726 (TA) |
681 (TA) |
636 (TA) |
630 (TA) |
578 (TA) |
576 (TA) |
572 (TA) |
523 (TA) |
524 | 525 | 526 | 527 | 501 (TA) |
502 | 502 (TA) |
| 45 | 1196 (TA) |
921 (TA) |
922 | 898 (TA) |
862 (TA) |
842 (TA) |
750 (TA) |
751 | 752 | 739 (TA) |
737 (TA) |
677 (TA) |
678 | 679 | 639 (TA) |
640 |
| 46 | 866 (GC) |
761 (GC) |
755 (GC) |
680 (GC) |
631 (GC) |
632 | 632 (GC) |
578 (GC) |
579 | 534 (GC) |
528 (GC) |
529 | 498 (GC) |
499 | 500 | 488 (GC) |
| 47 | 940 (TA) |
906 (TA) |
873 (TA) |
871 (TA) |
757 (TA) |
758 | 707 (TA) |
708 | 675 (TA) |
676 | 677 | 678 | 629 (TA) |
630 | 631 | 632 |
| 48 | 1214 (TA) |
935 (TA) |
936 | 925 (GC) |
926 | 774 (TA) |
775 | 776 | 777 | 733 (GC) |
734 | 703 (GC) |
667 (GC) |
668 | 669 | 654 (GC) |
| 49 | 1560 (TA) |
1389 (GC) |
1079 (TA) |
948 (TA) |
949 | 950 | 849 (TA) |
850 | 841 (TA) |
793 (TA) |
792 (TA) |
771 (TA) |
772 | 773 | 758 (TA) |
759 |
| 50 | 1391 (TA) |
1376 (TA) |
1342 (TA) |
1308 (TA) |
1085 (LL) |
1056 (TA) |
1057 | 1046 (TA) |
1036 (TA) |
1037 (TA) |
877 (TA) |
878 | 879 | 872 (TA) |
857 (TA) |
820 (TA) |
| 51 | 1503 (TA) |
1460 (TA) |
1295 (TA) |
1234 (TA) |
1235 | 1057 (TA) |
1049 (TA) |
848 (TA) |
849 | 850 | 851 | 852 | 853 | 854 | 855 | 856 |
| 52 | 1826 (TA) |
1404 (TA) |
1405 | 1401 (TA) |
1237 (TA) |
1235 (TA) |
1140 (TA) |
1141 | 1124 (TA) |
1125 | 1126 | 1082 (TA) |
1083 | 1084 | 1033 (TA) |
1034 |
| 53 | 1634 (TA) |
1606 (TA) |
1401 (TA) |
1345 (TA) |
1337 (TA) |
1180 (TA) |
1181 | 1163 (TA) |
1000 (TA) |
1001 | 1002 | 1003 | 998 (TA) |
999 | 903 (TA) |
904 |
| 54 | 1772 (TA) |
1582 (TA) |
1496 (TA) |
1477 (TA) |
1303 (TA) |
1225 (TA) |
1185 (TA) |
1186 | 1187 | 1127 (TA) |
1128 | 1107 (TA) |
1091 (TA) |
1092 | 1093 | 1062 (TA) |
| 55 | 1744 (TA) |
1745 | 1576 (TA) |
1454 (TA) |
1410 (TA) |
1352 (TA) |
1315 (TA) |
1191 (LL) |
1192 | 1193 | 1142 (TA) |
1143 | 1112 (TA) |
1113 | 1114 | 1059 (TA) |
| 56 | 1899 (TA) |
1775 (TA) |
1647 (TA) |
1583 (TA) |
1581 (TA) |
1582 (TA) |
1533 (TA) |
1476 (TA) |
1331 (TA) |
1332 | 1333 | 1334 | 1245 (TA) |
1206 (TA) |
1207 | 1208 |
| 57 | 2501 (FY) |
1908 (TA) |
1909 | 1800 (TA) |
1742 (TA) |
1702 (FY) |
1703 | 1704 (TA) |
1486 (TA) |
1487 | 1488 | 1489 | 1435 (TA) |
1436 | 1400 (TA) |
1308 (TA) |
| 58 | 2071 (TA) |
2072 | 1929 (TA) |
1926 (TA) |
1927 | 1903 (TA) |
1794 (TA) |
1795 | 1748 (TA) |
1739 (TA) |
1680 (TA) |
1605 (TA) |
1606 | 1607 | 1571 (TA) |
1572 |
| 59 | 2825 (TA) |
2492 (TA) |
2469 (TA) |
1858 (TA) |
1859 | 1860 | 1761 (TA) |
1747 (TA) |
1748 | 1648 (TA) |
1649 | 1650 | 1651 | 1542 (TA) |
1543 | 1544 |
| 60 | 2703 (LL) |
2256 (TA) |
2252 (TA) |
2185 (TA) |
1937 (TA) |
1938 | 1764 (TA) |
1765 | 1766 | 1767 | 1635 (TA) |
1636 | 1637 | 1633 (TA) |
1516 (TA) |
1517 |
| 61 | 1376216 (LL) |
1312877 (FY) |
600944 (FY) |
600515 (FY) |
600516 | 595259 (FY) |
593743 (FY) |
593744 | 593745 | 593722 (FY) |
593094 (FY) |
593095 | 593094 (FY) |
593090 (FY) |
593065 (FY) |
593066 |
| 62 | 717005 (LL) |
33411 (GC) |
33412 | 32192 (GC) |
24388 (GC) |
24389 | 24390 | 24391 | 24392 | 24342 (GC) |
24343 | 23960 (GC) |
23961 | 23962 | 23963 | 23311 (GC) |
| 63 | 52731 (LL) |
7491 (TA) |
4136 (TA) |
3684 (TA) |
3472 (TA) |
3473 | 3454 (TA) |
3393 (TA) |
3361 (TA) |
3357 (TA) |
3290 (TA) |
3291 | 3292 | 3291 (TA) |
3292 | 3270 (TA) |
| 64 | 4587 (TA) |
4195 (TA) |
4039 (TA) |
3393 (TA) |
3394 | 3395 | 3396 | 3247 (TA) |
3248 | 3192 (TA) |
3166 (TA) |
3162 (TA) |
3117 (TA) |
3118 | 3055 (TA) |
2944 (TA) |
| 65 | 3392 (TA) |
2810 (TA) |
2607 (TA) |
2585 (TA) |
2497 (TA) |
2498 | 2472 (TA) |
2334 (TA) |
2335 | 2186 (TA) |
2187 | 1948 (TA) |
1949 | 1950 | 1951 | 1952 |
| 66 | 5716 (TA) |
4224 (TA) |
3692 (FY) |
3426 (TA) |
3427 | 3428 | 3429 | 3295 (TA) |
3296 | 2917 (TA) |
2918 | 2831 (FY) |
2698 (TA) |
2699 | 2700 | 2701 |
| 67 | 6078 (TA) |
4672 (TA) |
4561 (TA) |
4273 (TA) |
3784 (TA) |
2518 (TA) |
2519 | 2520 | 2521 | 2448 (TA) |
2449 | 2450 | 2451 | 2452 | 2453 | 2454 |
| 68 | 7636 (LL) |
5612 (FY) |
4107 (TA) |
4044 (TA) |
3898 (TA) |
3595 (TA) |
3596 | 3597 | 2938 (LL) |
2939 | 2895 (TA) |
2896 | 2816 (TA) |
2817 | 2818 | 2819 |
| 69 | 5624 (TA) |
3885 (TA) |
3886 | 3605 (TA) |
3433 (TA) |
3033 (TA) |
3034 | 2979 (TA) |
2980 | 2981 | 2785 (TA) |
2770 (TA) |
2771 | 2772 | 2633 (TA) |
2634 |
| 70 | 6138 (LL) |
3949 (TA) |
3950 | 3625 (TA) |
3516 (TA) |
3517 | 3353 (TA) |
3141 (TA) |
2925 (TA) |
2926 | 2856 (TA) |
2857 | 2713 (TA) |
2645 (TA) |
2646 | 2647 |
| 71 | 5831 (TA) |
3815 (TA) |
3640 (TA) |
3575 (TA) |
3381 (TA) |
3382 | 3383 | 3313 (TA) |
3307 (TA) |
3308 | 2941 (TA) |
2942 | 2943 | 2944 | 2945 | 2946 |
| 72 | 4162 (TA) |
4163 | 3520 (TA) |
3521 | 3448 (TA) |
3449 | 3450 | 3451 | 3452 | 3453 | 3371 (TA) |
3372 | 3373 | 3228 (TA) |
3229 | 3230 |
| 73 | 843058 (GC) |
824787 (GC) |
473224 (GC) |
473225 | 473226 | 473227 | 473228 | 445078 (GC) |
445079 | 445080 | 445081 | 445082 | 445083 | 445084 | 445085 | 445086 |
| 74 | 527022 (LL) |
435176 (FY) |
435111 (FY) |
434497 (FY) |
434337 (FY) |
405358 (FY) |
405094 (FY) |
404463 (FY) |
404464 | 375560 (FY) |
375468 (FY) |
295807 (FY) |
295724 (FY) |
292897 (FY) |
292898 | 286316 (FY) |
| 75 | 9317 (TA) |
8909 (TA) |
8712 (TA) |
8362 (TA) |
8346 (TA) |
8317 (TA) |
8284 (TA) |
8257 (TA) |
8141 (TA) |
8142 | 8104 (TA) |
8105 | 8106 | 8107 | 8089 (TA) |
8090 |
| 76 | 7203 (TA) |
6812 (TA) |
5335 (TA) |
4712 (TA) |
4713 | 4495 (TA) |
4405 (TA) |
4381 (TA) |
4189 (TA) |
4098 (TA) |
4099 | 4081 (TA) |
4007 (TA) |
4008 | 3688 (TA) |
3689 |
| 77 | 11993 (TA) |
9055 (FY) |
5775 (TA) |
5776 | 5660 (TA) |
5361 (TA) |
5362 | 5363 | 5233 (TA) |
5234 | 5208 (TA) |
5099 (TA) |
5100 | 5024 (TA) |
5025 | 4845 (TA) |
| 78 | 16180 (TA) |
15668 (FY) |
15669 | 15163 (TA) |
9766 (FY) |
8658 (FY) |
8659 | 8593 (LL) |
6554 (LL) |
6555 | 5786 (FY) |
5787 | 5788 | 5789 | 5790 | 5635 (TA) |
| 79 | 7447 (TA) |
6057 (TA) |
5169 (FY) |
4974 (FY) |
4975 | 4840 (TA) |
4429 (TA) |
4430 | 4431 | 4182 (TA) |
4183 | 4184 | 4185 | 4071 (TA) |
4072 | 3882 (TA) |
| 80 | 8033 (TA) |
7845 (TA) |
6889 (TA) |
6890 | 6482 (TA) |
5832 (TA) |
5833 | 5590 (TA) |
4765 (TA) |
4703 (TA) |
4704 | 4705 | 4706 | 4707 | 4708 | 4644 (TA) |
| 81 | 7255 (TA) |
6652 (TA) |
6653 | 6562 (TA) |
6563 | 4634 (TA) |
4635 | 4636 | 4637 | 4638 | 4639 | 4640 | 3970 (TA) |
3890 (TA) |
3891 | 3715 (TA) |
| 82 | 11009 (TA) |
10490 (TA) |
8337 (TA) |
8338 | 7992 (TA) |
7993 | 7994 | 7655 (TA) |
7177 (TA) |
6997 (TA) |
6998 | 6521 (TA) |
6522 | 6510 (TA) |
6507 (TA) |
6508 |
| 83 | 17386 (LL) |
10356 (TA) |
8401 (TA) |
8211 (TA) |
8212 | 8213 | 7984 (TA) |
7985 | 7986 | 7795 (TA) |
7796 | 7351 (TA) |
7352 | 7353 | 6654 (TA) |
6655 |
| 84 | 7755 (TA) |
6822 (TA) |
6030 (TA) |
5883 (TA) |
5667 (TA) |
5668 | 5602 (TA) |
5450 (TA) |
5451 | 5452 | 5284 (TA) |
5285 | 5134 (TA) |
5135 | 4740 (TA) |
4741 |
| 85 | 42218 (TA) |
42048 (TA) |
40079 (TA) |
39960 (TA) |
39961 | 37913 (FY) |
37907 (FY) |
37861 (FY) |
37751 (FY) |
37752 | 37702 (FY) |
37703 | 37704 | 37705 | 37706 | 37707 |
| 86 | 23501 (TA) |
17847 (TA) |
16324 (TA) |
15231 (TA) |
14764 (TA) |
14346 (TA) |
14347 | 14348 | 14349 | 14350 | 14345 (TA) |
14211 (TA) |
14212 | 14213 | 14214 | 14215 |
| 87 | 9519 (TA) |
7777 (TA) |
7778 | 7456 (TA) |
6702 (TA) |
6511 (TA) |
6512 | 6482 (TA) |
6483 | 6484 | 6485 | 6384 (TA) |
6385 | 6386 | 6387 | 6328 (TA) |
| 88 | 14525 (FY) |
8923 (TA) |
8165 (TA) |
7071 (TA) |
7072 | 7073 | 7074 | 6791 (TA) |
6792 | 6793 | 6794 | 6795 | 6796 | 6688 (TA) |
6689 | 6690 |
| 89 | 12211 (TA) |
10709 (TA) |
9145 (TA) |
9146 | 7896 (TA) |
7897 | 7898 | 7833 (TA) |
7834 | 7835 | 7830 (TA) |
7527 (TA) |
7528 | 7529 | 7530 | 7531 |
| 90 | 14095 (TA) |
11153 (TA) |
10574 (TA) |
9848 (TA) |
9133 (TA) |
8594 (TA) |
8595 | 8596 | 8597 | 8598 | 8596 (TA) |
8239 (TA) |
8240 | 8241 | 7706 (TA) |
7707 |
| 91 | 18377 (TA) |
11084 (TA) |
9722 (TA) |
9310 (TA) |
9311 | 9123 (TA) |
9015 (TA) |
8868 (TA) |
8740 (TA) |
8741 | 8742 | 8743 | 8744 | 8692 (TA) |
8569 (TA) |
8486 (TA) |
| 92 | 20591 (TA) |
13490 (FY) |
13278 (TA) |
12036 (TA) |
12037 | 12038 | 11449 (TA) |
10694 (TA) |
10695 | 10696 | 9296 (TA) |
9297 | 9298 | 9299 | 9300 | 9301 |
| 93 | 15518 (TA) |
10703 (TA) |
10704 | 9585 (TA) |
9464 (TA) |
9465 | 9387 (TA) |
9388 | 8820 (TA) |
7425 (TA) |
7426 | 7427 | 7428 | 7429 | 7430 | 7431 |
| 94 | 15675 (TA) |
14127 (TA) |
13812 (TA) |
11347 (TA) |
8989 (TA) |
8933 (TA) |
8919 (TA) |
8920 | 8921 | 8922 | 8923 | 8924 | 8925 | 8314 (TA) |
8315 | 8316 |
| 95 | 13622 (TA) |
12560 (TA) |
11362 (TA) |
11043 (TA) |
11044 | 10510 (TA) |
10309 (TA) |
10310 | 10311 | 10312 | 10177 (TA) |
10178 | 10179 | 10180 | 9795 (TA) |
9796 |
| 96 | 25766 (TA) |
13620 (GC) |
12905 (GC) |
12811 (GC) |
11719 (TA) |
11210 (TA) |
10596 (TA) |
10597 | 10598 | 10599 | 10600 | 9989 (TA) |
9990 | 9991 | 9992 | 9993 |
| 97 | 53287 (TA) |
53179 (TA) |
52450 (TA) |
50315 (TA) |
49823 (TA) |
49824 | 49825 | 49826 | 49827 | 49828 | 49639 (TA) |
49640 | 49575 (TA) |
49554 (TA) |
49555 | 49463 (TA) |
| 98 | 25260 (FY) |
13529 (FY) |
13135 (TA) |
12704 (TA) |
12705 | 12706 | 12560 (TA) |
12561 | 12562 | 12563 | 12423 (TA) |
11503 (TA) |
11504 | 11505 | 11506 | 11211 (LL) |
| 99 | 32837 (LL) |
16234 (GC) |
15285 (GC) |
15286 | 14376 (GC) |
13336 (GC) |
13337 | 12452 (GC) |
12216 (GC) |
12217 | 12218 | 12171 (GC) |
11561 (LL) |
11562 | 11563 | 11564 |
| 100 | 21071 (TA) |
12217 (GC) |
12218 | 12219 | 12151 (GC) |
12152 | 12153 | 12154 | 11290 (GC) |
11291 | 11292 | 11130 (GC) |
11131 | 11132 | 11133 | 11134 |
| AN: Aleksi Niemelä | BS: Bob Scher | DA: David Alten | EB: Edward Brisse | EB2: Eric Bainville |
| FC: Frank Clowes | GR: Giovanni Resta | JC: Joe Crump | JCM: Jean-Charles Meyrignac | JMC: John Michael Crump |
| JML: Joe MacLean | 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 | ML: 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 | FY: Fumitaka Yura |
| DM: Douglas McNeil |
| k | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 |
| m+n | 97 (TA) |
101 (TA) |
108 (GC) |
113 (TA) |
111 (TA) |
123 (LL) |
116 (TA) |
141 (TA) |
146 (TA) |
156 (TA) |
173 (TA) |
173 (TA) |
175 (TA) |
198 (TA) |
211 (TA) |
204 (TA) |
218 (TA) |
| k | 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 | 61 | 62 | 63 | 64 | 65 | 66 |
| m+n | 232 (TA) |
255 (TA) |
273 (TA) |
279 (TA) |
280 (TA) |
295 (TA) |
322 (TA) |
317 (GC) |
348 (TA) |
365 (LL) |
339 (LL) |
362 (TA) |
382 (GC) |
402 (TA) |
444 (FY) |
464 (LL) |
495 (LL) |
| k | 67 | 68 | 69 | 70 | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 | 81 | 82 | 83 |
| m+n | 514 (TA) |
556 (TA) |
578 (GC) |
607 (GC) |
610 (GC) |
684 (LL) |
570 (GC) |
680 (GC) |
727 (GC) |
760 (LL) |
815 (GC) |
770 (GC) |
843 (GC) |
905 (LL) |
887 (FY) |
905 (GC) |
985 (LL) |
| k | 84 | 85 | 86 | 87 | 88 | 89 | 90 | 91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 |
| m+n | 1019 (LL) |
1048 (GC) |
1048 (GC) |
1074 (LL) |
1225 (GC) |
1288 (LL) |
1266 (LL) |
1312 (GC) |
1382 (LL) |
1339 (LL) |
1489 (GC) |
1699 (LL) |
1412 (GC) |
1453 (GC) |
1522 (GC) |
1621 (GC) |
1654 (GC) |
| 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 |