## Wol4 93, 94

``` Subject: Wolstenholme 4 factors
Date: Fri, 20 Nov 1998 13:54:49 +0000
From: Allan MacLeod <MACL-MS0@wpmail.paisley.ac.uk>
To: kc2h-msm@asahi-net.or.jp

Hello again,

You introduced the Wolstenholme 3 and 4 numbers recently.

The following two factors should be of interest.

Allan MacLeod

(a) Wolstenholme 4 - with n=94

Input number is
16308573088521616563226537017430534564465823715260476422000128903616987738298432825972851537531695978274666822014304794320707116052775989217462799179 (149 digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=469812695

Step 1 took 3479330ms for 39070093 muls, 3 gcdexts

Step 2 took -2646678ms for 16480797 muls, 29004 gcdexts

********** Factor found in step 2: 401428769488552579706116617333217

Found probable prime factor of 33 digits: 401428769488552579706116617333217

Composite cofactor
40626318610148052947037514161391710285597811738865016685424103958998292433336039845263803419061445974913083769442987 has 116 digits

(b) Wolstenholme 4 - n=93

Input number is
356575634892489177898614067667874251448880737949743366394355139796916124801801319520303916492719530191166545418732511706118823 (126 digits)

Using B1=1000000, B2=100000000, polynomial x^18, sigma=1475585527
Step 1 took 1863461ms for 12986907 muls, 3 gcdexts
Step 2 took 935275ms for 5771003 muls, 12687 gcdexts

********** Factor found in step 2: 254928443224114335245809

Found probable prime factor of 24 digits: 254928443224114335245809

Composite cofactor
1398728326987876000585166847803276155660527898845921096567461338512987055966141182803621357984723956247 has 103 digits
```

E-mail : kc2h-msm@asahi-net.or.jp
Hisanori Mishima