ECM Factorization applet records
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- Number Theory
- ECM Factorization applet records
In June 2025, I changed the calculator to optimize the bounds for the different curves. So, now it would be easier to find bigger prime factors.
New calculator
| Rank (Digits) | Number (Curve) | Prime factor | Discoverer |
|---|---|---|---|
| 1 (62) | [9] (275619) | 47 5009613080 9856312395 3446535558 0582490621 3244273346 3363231771 | Andrea Fanchini (3 May 2026) |
| 2 (62) | 81 + 82 × 8384 (325180) | 20 4726624838 9052049770 7918193874 0911084915 0883963607 5460563113 | Karl Vago (3 Jul 2025) |
| 3 (55) | 62959 − 1 (117072) | 72308 8012752682 1693925059 5089720829 5270213300 4552346281 | Andrea Fanchini (31 Aug 2025) |
| 4 (50) | 4 × 10130 − 31 (60608) | 8231638827 1718992535 4938548549 0246263219 3974477977 | Andrea Fanchini (14 Dec 2025) |
| 5 (48) | 4 × 10181 − 13 (46844) | 72606716 5586600200 4269946916 9472858870 6768743169 | Andrea Fanchini (23 Nov 2025) |
| 6 (48) | 4 × 10159 + 41 (36826) | 21855192 0024031168 9277736976 6180953874 5109102567 | Andrea Fanchini (14 Dec 2025) |
| 7 (47) | 10169 + 53 (7920) | 2254787 3392796789 0874517505 0982982129 4031082489 | Andrea Fanchini (8 Nov 2025) |
| 8 (46) | 21 × 10129 − 12 (27839) | 678348 7931725003 4707712482 5952002306 4463941573 | Andrea Fanchini (16 Nov 2025) |
| 9 (45) | 25 × 10123 − 52 (11169) | 59819 8813857493 4840491021 3378011518 4139309979 | Andrea Fanchini (8 Nov 2025) |
| 10 (45) | 10157 + 53 (13884) | 35328 0588885973 2860428261 9304852885 2252476239 | Andrea Fanchini (16 Nov 2025) |
| 11 (44) | 4 × 10147 + 41 (13394) | 6817 2780040916 6398988619 5765228705 2127187331 | Andrea Fanchini (8 Nov 2025) |
| 12 (44) | 43 × 10133 − 34 (22048) | 5614 6570871964 6451240812 2110359327 7182795413 | Andrea Fanchini (16 Nov 2025) |
| 13 (43) | (23 × 10121 − 32)/99 (8312) | 142 4472529644 0497695051 4324390354 1893457857 | Andrea Fanchini (1 Nov 2025) |
| 14 (42) | 2 × 10163 + 61 (9284) | 76 1860097003 0617756095 7493494352 4755379623 | Andrea Fanchini (8 Nov 2025) |
| 15 (42) | 10111 + 7596549774630 (6154) | 75 7701748351 2809446008 5247190938 1913866069 | A. Weiss (9 Oct 2025) |
| 16 (41) | (10142 − 1) / 9 (5909) | 4 5994811347 8868463102 2172889522 3034301839 | Matt Stath (5 Jun 2026) |
| 17 (41) | 2322 + 2161 + 41 (401) | 1 2720407227 9868635662 0320505006 6962019199 | Matt Stath (15 Jan 2026) |
| 18 (41) | P(2900) × P(3101) (3095) | 1 1687201387 8709061513 0730893284 0302329479 | Matt Stath (17 Aug 2025) |
| 19 (40) | (20260608 × 105)15 + 1 (2968) | 8946714110 8942800635 5486300074 0383736481 | Matt Stath (11 Jun 2026) |
| 20 (40) | 4 × 10173 + 41 (2629) | 3690261951 4174349289 8270871491 0132460751 | Andrea Fanchini (2 Nov 2025) |
Old calculator
| 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) | [2] (172579) | 1200 0000000000 0000000000 0618000000 0000000000 0000007957 | Andrea Fanchini (14 Apr 2025) |
| 8 (54) | 76 + 77 × 7879 (142787) | 1164 9984183323 8338672209 4424392492 9760503370 1935129681 | Karl Vago (31 May 2023) |
| 9 (53) | [3] (7294) | 675 0000000000 0000000000 0130500000 0000000000 0000000631 | Andrea Fanchini (26 Jan 2025) |
| 10 (53) | [4] (2559) | 663 8555879669 8718889062 8832756378 5433338498 0160804713 | Matt Stath (24 Aug 2021) |
| 11 (53) | 74 + 75 × 7677 (648013) | 352 5917125041 7642224913 6522232665 3485687685 1696267951 | Karl Vago (21 Jul 2022) |
| 12 (52) | 314159 26535897938+1 (2398) | 79 7383280806 2132692406 8566997093 0335243720 8326360369 | Matt Stath (18 Jun 2022) |
| 13 (52) | [5] (39844) | 77 9193059338 5727999316 1219016061 3324119121 4619322903 | Yinon Giladi (29 Jun 2023) |
| 14 (52) | [6] (150665) | 12 0000000000 0000000000 0023400000 0000000000 0000001141 | Andrea Fanchini (8 Feb 2025) |
| 15 (51) | 69 + 70 × 7172 (19049) | 6 2940242187 4852186463 2068442633 6674105792 3282571661 | Karl Vago (1 Jul 2009) |
| 16 (51) | 2395 − 1 − 2 × 29696 (74764) | 5 2076674035 5791336037 1954793855 7867765495 8470159341 | Matt Stath (19 Jul 2019) |
| 17 (51) | P(14928)+P(11112) (6329) | 4 0001754371 2284963904 9292289971 4267050730 0079442083 | Matt Stath (27 Feb 2019) |
| 18 (51) | [7] (141248) | 3 0000000000 0000000000 0019500000 0000000000 0000003169 | Andrea Fanchini (8 Feb 2025) |
| 19 (51) | 75 × 75! + 1 (189727) | 2 9207004861 0934088266 0671772322 3470882179 0251951617 | Matt Stath (12 Jan 2023) |
| 20 (51) | [8] (256420) | 2 7500000000 0000000000 4457750000 0000000000 0180650319 | Andrea Fanchini (8 Feb 2025) |
[1]: 3141592 6535897932 3846264338 3279502884 * 2^256+1
[2]: 9*(4*10^27+83)^2*(4*10^26+103)^2+3*(4*10^27+83)^2+3*(4*10^26+103)^2+1
[3]: 9*(3*10^27+88)^2*(3*10^26+29)^2+3*(3*10^27+88)^2+3*(3*10^26+29)^2+1
[4]: (((10^39-1)/9)*2^128+1)*((F(78))*2^128-1)
[5]: 121 3159696991 8642172061 2104850940 3991328110 3522796501 6283179014 1133866279 6963947436 4737088304 9929870323
[6]: 9*(10^27+14)^2*(4*10^25+39)^2+3*(10^27+14)^2+3*(4*10^25+39)^2+1
[7]: 9*(2*10^26+158)^2*(2*10^25+65)^2+3*(2*10^26+158)^2+3*(2*10^25+65)^2+1
[8]: 121*(10^26+374)^2*(10^25+8105)^2+11*(10^26+374)^2+11*(10^25+8105)^2+1
[9]: 8497 6156583472 0455649473 6253651654 0188614392 2081871757 9377002421 4384751177 4006428267 8094142498 7070918222 4810243787
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.