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
63 501833346224699945415734599188794254249073816054295913096772683
2 * 3 * 431 * 6553 * 92801 * 83330041 * 909258899 * 1053137819 * 1429493837 * 2797573591939277
23*10268-14 S. Troisi 03.01.2024 1010 1016
59 73204686656099026837146535540627040826623006059063005923089
24 * 3 * 11 * 13 * 31 * 2797 * 12527 * 56941 * 213079 * 363269 * 274212791 * 816574271 * 9949079341303
46*10269+35 S. Troisi 27.12.2023 109 1013
59 26517525424793828934845006281880174225095142892711732758207
2 * 9733 * 36905801 * 179753251 * 181111481 * 1577439593 * 3519792481 * 204206286217
83*10276+43 S. Troisi 05.01.2024 1010 1012
59 12798830540286697738097001413455268308836003073182603569933
22 * 17 * 59 * 107 * 113 * 20414117 * 223034797 * 269477639 * 439758239 * 481458247 * 1015660517
806900026039997902396314117-1 A. Kruppa 30.06.2011 109 1010
58 1850475917485872002512582039081380045643275936063486278441
23 * 5 * 37 * 71 * 139 * 281 * 1093 * 16553 * 90997 * 22020091 * 263251856411 * 47241942823345729
216553-1 A. Repko 19.10.2023 1012 1017
58 1372098406910139347411473978297737029649599583843164650153
23.32.1049.1627.139999.1284223.7475317.341342347.2456044907.9909876848747
22098+1 P. Zimmermann 28.09.2005 (*) 1010 1013
58 1061218320930836033815677839864965802389619522580761600137
23 * 3 * 29 * 133919 * 539093 * 702539 * 8906617 * 516476143 * 852256543 * 7668064972279
2133919-1 O. Kruse 12.10.2023 109 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

#### 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
57 357561419933316305231935975632510092006707198190314688497 6396+1 P. Zimmermann 31.10.2003 (*) 109 1012
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.