Collated by Paul Zimmermann | Record Factors Found By Pollard's p-1 Method | thanks to Andy Steward |
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This method of integer factorisation was first published by J.M.Pollard in 1974 ("Theorems on Factorization and Primality Testing" Proc. Camb. Phil. Soc., volume 76, pages 521-528).
It can find a large factor p very quickly if it should happen that p-1 is composed of small factors.
This table lists the 10 largest factors found by this method of which I am aware (lines with an asterix design factors that were at one time the current record). If you know of any others, please email me at zimmerma at loria dot fr. Note that the values of B1 and B2 shown here are the minimum power of ten needed to have found the factor and not necessarily the ones actually used by the finder.
Digits | p p-1 | Factor Of | Found By | Date | B1 | B2 |
---|---|---|---|---|---|---|
66 | 672038771836751227845696565342450315062141551559473564642434674541 22.3.5.7.17.23.31.163.401.617.4271.13681.22877.43397.203459.1396027.6995393.13456591.2110402817 | 960119-1 | T. Nohara | 29.06.2006 (*) | 108 | 1010 |
64 | 1939611922516629203444058938928521328695726603873690611596368359 2 * 3 * 11 * 1187 * 9233729 * 13761367 * 43294577 * 51593573 * 100760321 * 379192511 * 2282985164293 | 10243-4*10121-1 | M. Tervooren | 13.09.2012 | 109 | 1013 |
59 | 12798830540286697738097001413455268308836003073182603569933 22 * 17 * 59 * 107 * 113 * 20414117 * 223034797 * 269477639 * 439758239 * 481458247 * 1015660517 | 806900026039997902396314117-1 | A. Kruppa | 30.06.2011 | 109 | 1010 |
58 | 1372098406910139347411473978297737029649599583843164650153 23.32.1049.1627.139999.1284223.7475317.341342347.2456044907.9909876848747 | 22098+1 | P. Zimmermann | 28.09.2005 (*) | 1010 | 1013 |
57 | 597675141714287694105985276757270027085238116805223111681 210.5.7.17.19.31.101.3259.1419689.3766709.11459431.533006401.154908937836101 | 5323+2323 | P. Jammes | 06.04.2012 | 109 | 1015 |
57 | 357561419933316305231935975632510092006707198190314688497 24.32.11.31.612.2131.7703.102199.12170281.294393133.346193663.940452192083 | 6396+1 | P. Zimmermann | 31.10.2003 (*) | 109 | 1012 |
57 | 158598051875658496019605045735778598245626251920942535281 24.5.13.4397.28001.55819.104207.77838899.144518893.1402974751.13492250351 | 11260+1 | P. Zimmermann | 28.03.2004 | 1010 | 1011 |
57 | 102865672608413943106458586567808781654205261348077885949 22 * 35 * 412 * 47 * 9319 * 295357 * 84406703 * 425895553 * 684792803 * 19768914564757 | 9515341-1 | A. Reich | 31.12.2012 | 109 | 1014 |
55 | 4090528046283359170676873346935001420047744892805041229 22 * 32 * 7 * 41 * 211 * 383 * 5189 * 24133 * 910451 * 113117987 * 472409801 * 804102884120257 | 8190141-1 | A. Reich | 12.03.2015 | 109 | 1015 |
55 | 2997347544642661833497896836795494793702018162645139063 2 * 3 * 1637 * 1669 * 36919 * 470941 * 3195433 * 54508211 * 325206701 * 185657832242317 | 236919-1 | nordi | 23.05.2022 | 109 | 1015 |
Digits | p | Factor Of | Found By | Year | B1 | B2 |
---|---|---|---|---|---|---|
34 | 7146831801094929757704917464134401 | F575 | Montgomery/Silverman | 1989 (*) | 107 | 108 |
32 | 49858990580788843054012690078841 | 2977-1 | R. Brent | October 1984 (*) | 107 | 108 |