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 Subject: 
    Date: 4 Dec 1997 08:33:14 -0000 
    From: yamasaki@kusm.kyoto-u.ac.jp
      To: kc2h-msm@asahi-net.or.jp

                           Factors of N# + 1

N!, or N factorial, may be defined as the product of all integers between
1 and N inclusive.  N#, or N primorial, is defined as the product of all
primes up to and including N.  Easy proofs of the infinity of primes
arise from considering the possible factors of N# +/-1 and N! +/- 1.

In the table below, Pxxx denotes a prime of xxx decimal digits and Cyyy a
composite of yyy decimal digits.

This table was begun by George Sassoon, geosas@aol.com, who discovered
most of the factors below.  Other folk who deserve credit are Vivian
Stevens (viv@ictus.demon.co.uk), Sam Wagstaff (ssw@cs.purdue.edu) and
Paul Leyland (pcl@oucs.ox.ac.uk).

  N     Factors of N# + 1

  2     3
  3     7
  5     31
  7     211
 11     2311
 13     59.509
 17     19.97.277
 19     347.27953
 23     317.703763
 29     331.571.34231
 31     200560490131
 37     181.60611.676421
 41     61.450451.11072701
 43     167.78339888213593
 47     953.46727.13808181181
 53     73.139.173.18564761860301
 59     277.3467.105229.19026377261
 61     223.525956867082542470777
 67     54730729297.143581524529603
 71     1063.303049.598841.2892214489673
 73     2521.16156160491570418147806951
 79     22093.1503181961.96888414202798247
 83     265739.1004988035964897329167431269
 89     131.1039.2719.64225891884294373371806141
 97     2336993.13848803.71237436024091007473549
101     960703.242387464553038099079594127301057
103     2297.9700398839.179365737007.6001315443334531
107     149.13203797.30501264491063137.42767843651083711
109     334507.1290433.648046444234299714623177554034701
113     5122427.2025436786007.3046707595069540247157055819
127     1543.49999.552001.57900988201093.1628080529999073967231
131     1951.22993.11723231859473014144932345466415143728266617
137     881.1657.32633677.160823938621.5330099340103.1764291759303233
139     678279959005528882498681487.14764768614544245139224580493
149     87549524399.65018161573521013453.262140076844134219184937113
151     23269086799180847.9683213481319911991636641541802024271084713
157     1381.1867.8311930927.38893867968570583.42440201875440880489113304753
163     1361.214114727210560829.32267019267402210517.613228865630544238382107
167     205590139.53252429177.7064576339566763.12450154709928940906197946067239
173     62614127.2660580156093611580352333193927566158528098772260689062181793
179     601.1651781.8564177.358995947.1525310189119.    P34
181     107453.5634838141.      P58
191     32999.175603474759.77148541513247.      P46
193     21639496447.7979125905967339495018877.  P43
197     521831.50257723.1601684368321.39081170243262541027.     P35
199     467.10723.57622771.5876645549.9458145520867.    P45
211     1051.2179.16333.43283699.75311908487.292812710684839.   P41
223     13867889468159. P74
227     3187.31223.1737142793.11463039340315601.973104505470446969309113.       P32
229     126173.495056820952423648923564303249326797.    P51
233     5981.32933.35077871.226523119.  P70
239     313.7174645079748110122986720794600650220537699.        P51
241     3499.23154953.14209707448699806612680132420076872871953.        P48
251     2963206058339377313.    P83
257     34259.948293.3733159.335215943.62633748760943.  P64
263     271.19891019.3957327431.25098482428840021840888422712477.       P55
269     17291.805843.531489841545151.   P84
271     15559.3423571.7683041.57470069653.      P83
277     243233. C108
281     62131.154236286097.2254306890769.1983989029829662277517988545921869.    P54
283     307.2111.4931.9484896326989.    P96
293     397773559.287683675991534887.10070764744578881500043.212536532647480887561479147.       P46
307     45029582471.82268833403.        P102
311     60722339.57620579376482127166154112047. P89
313     3761.582307223.4286054032039546304836890894583.68396136787144717561091841779546774293.  P47
317     131409329.3297118571963.27893824618337613620879631211.5915036078238665768300503768754291.       P48
331     8089.514757.369688343.1553606101.232407306191143.       P92
337     38453.  C131
347     1579.4793361871924428403.       C116
349     44953.141817427570657.  C122
353     2143.2659.195991.388277.2623573.        C119
359     11041477.15329443.40829741150863579.    C115
367     51420888649203007716619883183.  C120
373     4973.365313997.25276968433343666948419739.      P113
379     P154
383     C156
389     216401.4415819.906077190456575539.      C129
397     8629.10091.251144057.78931425554466677. P128
401     356647.106472237.176879825310092531660311384621.        C121
409     13314787.2687493999689.1207499319227522718393192409.    P120
419     1996109.12057377.148015898637479.6900895672359645977.   P123
421     2251.   C169
431     215983.321247.666143.22300450379.       P148
433     2089.1702001166295564185254173813.      C147
439     1291.6673.139650775093. C162
443     463.4889.856949461054094326679441.      C152
449     10567.1770997.4611953063.2076514060559.473511977621365483.583579995758527221397.2766671858089535693493463559207.        P84
457     C188
461     44159768129.    C180
463     983.190369.729293.100282859827.398078244463.1107468799967598177002554891344421. C123
467     718713552547.   C184
479     154491616237417891.     C181
487     11587.199739.9057272859117914235451.    P170
491     14419.247369.521723.12640654570543.     C176
499     827.13221604619.502039587537773.        C179

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