ECM Factorization applet records

  1. Alpertron
  2. Number Theory
  3. ECM Factorization applet records
Rank (Digits)Number (Curve)Prime factorDiscoverer
1 (62)10111 + 94 (26877)34 2605225331 9431214169 9016768017 3760465793 7085827437 1908475849Eino Lindfors (22 Jun 2011)
2 (59)18 + 3181 (914151)246096154 3985554500 7865829059 8948258532 5533968286 3740988001Robert J DuChateau (2 Mar 2011)
3 (56)24 + 2981 (210438)345039 2868697084 2350938851 3770443531 6756669757 8436905273Robert J DuChateau (17 Sep 2010)
4 (56)10151 − 1 (413220)286565 5283757454 6515657117 3601919711 4021191078 8651135283Alfred Eichhorn (9 Aug 2013)
5 (55)10193 − 1 (426141)20107 3479723774 1296291807 4804784644 5181353879 0168907747Alfred Eichhorn (9 Aug 2013)
6 (54)[1] (49187)1677 5606531588 2837707890 8144773302 3430902725 4223867371Matt Stath (22 Jul 2021)
7 (53)[2] (2559)663 8555879669 8718889062 8832756378 5433338498 0160804713Matt Stath (24 Aug 2021)
8 (53)74 + 75 × 7677 (648013)352 5917125041 7642224913 6522232665 3485687685 1696267951Karl Vago (21 Jul 2022)
9 (52)314159 26535897938+1 (2398)79 7383280806 2132692406 8566997093 0335243720 8326360369Matt Stath (18 Jun 2022)
10 (51)69 + 70 × 7172 (19049)6 2940242187 4852186463 2068442633 6674105792 3282571661Karl Vago (1 Jul 2009)
11 (51)2395 − 1 − 2 × 29696 (74764)5 2076674035 5791336037 1954793855 7867765495 8470159341Matt Stath (19 Jul 2019)
12 (51)P(14928)+P(11112) (6329)4 0001754371 2284963904 9292289971 4267050730 0079442083Matt Stath (27 Feb 2019)
13 (51)[3] (8764)1 9055077460 7843661856 2252514142 6710394976 3693861403Matt Stath (21 Jan 2021)
14 (51)P(11867) (113880)1 3780678595 0080013787 5802986179 4072559473 6611979839Matt Stath (5 Mar 2022)
15 (51)10101 − 56993 (164419)1 1782454340 0831857004 2642818908 5916894417 2987388481Matt Stath (1 Apr 2022)
16 (51)102! − 103 (56777)1 0838319563 5476009638 2881001964 6958141460 0272495833John S. Tilley (13 Jan 2011)
17 (51)[4] (44585)1 0044423154 1200332362 3387050678 0105229272 2559369439Hans Havermann (13 May 2013)
18 (50)12 + 3179 (21743)9977058037 1549319977 6419274219 6989303806 6678558689Robert J DuChateau (27 Jun 2010)
19 (50)RSA-100 (24420)3797522793 6943673922 8088727554 4562785456 5536638199Matt Stath (22 Jan 2015)
20 (50)1099 − 2783 (18936)3108480161 2134411476 3336994966 2780217266 0847517087Matt Stath (24 Feb 2020)

[1]: 3141592 6535897932 3846264338 3279502884 * 2^256+1

[2]: (((10^39-1)/9)*2^128+1)*((F(78))*2^128-1)

[3]: ((10^(27*4)-1) / (10^4-1)) * 18880 + 1

[4]: 111 2528084834 1926131034 7225322250 8134352891 7084094099 4552816159 4308489918 7364599082 4308676781 9738061751 (term #6612 of https://oeis.org/A195264)

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.