ECM Factorization applet records
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- Number Theory
- ECM Factorization applet records
| Rank (Digits) | Number (Curve) | Prime factor | Discoverer |
|---|---|---|---|
| 1 (62) | 10111 + 94 (26877) | 34 2605225331 9431214169 9016768017 3760465793 7085827437 1908475849 | Eino Lindfors (22 Jun 2011) |
| 2 (59) | 18 + 3181 (914151) | 246096154 3985554500 7865829059 8948258532 5533968286 3740988001 | Robert J DuChateau (2 Mar 2011) |
| 3 (56) | 24 + 2981 (210438) | 345039 2868697084 2350938851 3770443531 6756669757 8436905273 | Robert J DuChateau (17 Sep 2010) |
| 4 (56) | 10151 − 1 (413220) | 286565 5283757454 6515657117 3601919711 4021191078 8651135283 | Alfred Eichhorn (9 Aug 2013) |
| 5 (55) | 10193 − 1 (426141) | 20107 3479723774 1296291807 4804784644 5181353879 0168907747 | Alfred Eichhorn (9 Aug 2013) |
| 6 (54) | [1] (49187) | 1677 5606531588 2837707890 8144773302 3430902725 4223867371 | Matt Stath (22 Jul 2021) |
| 7 (54) | 76 + 77 × 7879 (142787) | 1164 9984183323 8338672209 4424392492 9760503370 1935129681 | Karl Vago (31 May 2023) |
| 8 (53) | [2] (2559) | 663 8555879669 8718889062 8832756378 5433338498 0160804713 | Matt Stath (24 Aug 2021) |
| 9 (53) | 74 + 75 × 7677 (648013) | 352 5917125041 7642224913 6522232665 3485687685 1696267951 | Karl Vago (21 Jul 2022) |
| 10 (52) | 314159 26535897938+1 (2398) | 79 7383280806 2132692406 8566997093 0335243720 8326360369 | Matt Stath (18 Jun 2022) |
| 11 (52) | [3] (39844) | 77 9193059338 5727999316 1219016061 3324119121 4619322903 | Yinon Giladi (29 Jun 2023) |
| 12 (51) | 69 + 70 × 7172 (19049) | 6 2940242187 4852186463 2068442633 6674105792 3282571661 | Karl Vago (1 Jul 2009) |
| 13 (51) | 2395 − 1 − 2 × 29696 (74764) | 5 2076674035 5791336037 1954793855 7867765495 8470159341 | Matt Stath (19 Jul 2019) |
| 14 (51) | P(14928)+P(11112) (6329) | 4 0001754371 2284963904 9292289971 4267050730 0079442083 | Matt Stath (27 Feb 2019) |
| 15 (51) | 75 × 75! + 1 (189727) | 2 9207004861 0934088266 0671772322 3470882179 0251951617 | Matt Stath (12 Jan 2023) |
| 16 (51) | [4] (8764) | 1 9055077460 7843661856 2252514142 6710394976 3693861403 | Matt Stath (21 Jan 2021) |
| 17 (51) | P(11867) (113880) | 1 3780678595 0080013787 5802986179 4072559473 6611979839 | Matt Stath (5 Mar 2022) |
| 18 (51) | 10101 − 56993 (164419) | 1 1782454340 0831857004 2642818908 5916894417 2987388481 | Matt Stath (1 Apr 2022) |
| 19 (51) | 102! − 103 (56777) | 1 0838319563 5476009638 2881001964 6958141460 0272495833 | John S. Tilley (13 Jan 2011) |
| 20 (51) | [5] (44585) | 1 0044423154 1200332362 3387050678 0105229272 2559369439 | Hans Havermann (13 May 2013) |
[1]: 3141592 6535897932 3846264338 3279502884 * 2^256+1
[2]: (((10^39-1)/9)*2^128+1)*((F(78))*2^128-1)
[3]: 121 3159696991 8642172061 2104850940 3991328110 3522796501 6283179014 1133866279 6963947436 4737088304 9929870323
[4]: ((10^(27*4)-1) / (10^4-1)) * 18880 + 1
[5]: 111 2528084834 1926131034 7225322250 8134352891 7084094099 4552816159 4308489918 7364599082 4308676781 9738061751 (term #6612 of https://oeis.org/A195264)
The numbers 1099 − 2783 and 10101 − 56993 are the largest numbers whose size is 99 and 101 digits respectively that are factored in two prime numbers of the same size. They were found by David Cleaver. Look at Brilliant numbers Web page.
The page lists the top 20 prime factors of numbers factorized by the applet after March 6th, 2003. These factors can be generated by the Web application by entering the curve number in the lower left input box after entering the number to be factored.
If you find a larger prime factor found by ECM factoring, please send me the data as shown in the table above (or the complete factorization if you wish). The curve number can be seen by clicking on the "verbose mode" check box. Notice that the curve number must be just after the number greater than the 20th in the ranking. If the number does not have a curve number at the right, it was found by division, so it does not count for the ECM records.