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
58 1372098406910139347411473978297737029649599583843164650153
23.32.1049.1627.139999.1284223.7475317.341342347.2456044907.9909876848747 		22098+1 P. Zimmermann 28.09.2005 (*) 1010 1013
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
53 20489047427450579051989683686453370154126820104624537
23.3.71.90107.4959947.7216081.16915319.17286223.12750725834505143 		24142+1 A. Kruppa
P. Montgomery 		18.01.2008 108 1017
52 7506686348037740621097710183200476580505073749325089
25.59.11329.22807.480587.14334767.89294369.4649376803.5380282339 		68118+1 CWI 11.07.2007 1010 1010
51 225024267640198977569930286413453544441731198242501
22.3.54.11.17.19.41.79.2711.6563.9041.15101.55763.132059.145501.1001677057 		1882+1 Martin 18.03.2007 106 1010
51 167830135284167673677615633207649147158544158899609
23.32.7.11.59.641.13711.34297.63997.473659.5541251.3789427.2674266229 		L(3717) H. Bock 18.06.2004 107 1010
51 157986592313618298072803274748393917349697502507301
22.3.52.17.19.29.1549.4519.2592593.402497231.491813681.15649730066921 		F1653 H. Bock 28.04.2006 109 1014
50 85342016175328920894457025833502015551241119114501
22.3.53.7.112.59.149.1129.32497.97157213.17065437931.125608853327081 		L4235 A. Kruppa
P. Montgomery 		01.11.2007 1011 1015

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.