Collated by
Paul Zimmermann

## Record Factors Found By Pollard's p-1 Method

thanks to Andy Steward
[P+1] [ECM]

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
54 762567327007985243550794651781955489819341685725481873
24 * 32 * 17 * 131 * 271 * 307 * 26729 * 95267 * 180179 * 8225579 * 266778469 * 28388418037841
p713-1 A. Kruppa 31.03.2011 109 1014
Note: p71 = 21649018537415721070808944353787377935616657106553962830422139559433239 divides 109371-1

#### Previous records

We list here only the factors that were first at a given time (to our best knowledge), for historical interest.
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

#### Notes

1. Fn is the nth number in the Fibonacci sequence.