| Collated by Paul Zimmermann | Record Factors Found By Pollard's p-1 Method | thanks to Andy Steward |
|---|
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 |
| 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 |