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 Subject: 
    Date: 4 Dec 1997 08:33:10 -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       1
3       5
5       29
7       11.19
11      2309
13      30029
17      61.8369
19      53.197.929
23      37.131.46027
29      79.81894851
31      228737.876817
37      229.541.1549.38669
41      304250263527209
43      141269.92608862041
47      191.53835557.59799107
53      87337.326257.1143707681
59      27600124633.69664915493
61      1193.85738903.1146665184811
67      163.2682037.17975352936245519
71      260681003321.2140320249725509
73      313.130126775077472920609013813
79      163.2843.154050371.45072420668688011
83      139.26417.72730720785932715377476303
89      P35
97      66683.34575048572282567142346657278943
101     2990092035859.77877992237653703381046191
103     15649.142067.4599659.2345476528134511293575297
107     17515703.21871237.2463838256443.2718987378107653
109     719.2963.33637693242743.3903552776732446839822199
113     295201.567840892706882863.188573541523110659271203
127     15098753.53836523233421347.4938679937132087522704219
131     10172884549.141929971892850488111.364235297758479811711
137     20962699238647.245652323403761.13991128678227301652750227
139     4871.20988504343363646127926611.97957120305761011573774669
149     673.448045542064369.4948626474214096948642213863754187837657
151     311.409.24083.73553706686333095518730694000692449365670934668377
157     1409.212909.41204155505831.2861886907783199742338113523322848541079
163     1291.2565890287.5869655087.296557694065995104962797259705798672615771
167     331.443.2324921219.9966924050498910251857.283401055985955918267159853871
173     1450184819.70130101304951.1638026247818646257156883948600783993669082361
179     23497.10508085821.31376977774573.962389165640406763213. P22
181     711427.38746702321.1231393632556286622892198907.        P30
191     521.483209.1581363911.15414974591.      P48
193     673.65473937.566471804985844321.        P49
197     519577.13170522280541.10639208937288223.        P45
199     1372062943.4784328604523758357.619780408302187874237918207.     P28
211     56543.110654059.70587793986617. P58
223     811.    P84
227     182309.75057984242015536975478208351523.        P52
229     53077.5497565129461239035650709608982319328127. P47
233     641.    P91
239     349.9491.39993893.      P82
241     389.89644308483145450484697016758269.   P64
251     565921.91679677.15700021586055397160311310308325895690972977.   P44
257     777041. P98
263     1176221.841626607.6174446933.   P81
269     757.142771.12318911453427703.   P84
271     2341.4261.27922541.42697366619.3881590179124452191153083.20996638941932036180486431.    P36
277     44753.248161.786431.    P98
281     303665792864057405074693.117277141037621524016699418297213730021625341. P48
283     7027.12575441052481.    P101
293     4111.166748157677124857.1217670675652709713577568997.   P73
307     1571.1847.      C117
311     166661291.4886278425797257511145616469. P90
313     917337320621.11992468992157.    P103
317     P131
331     7037216702504839.       C117
337     P136
347     1609.   C135
349     33409.  C136
353     18422659.41160337.183289461261013.216281814742687.      P100
359     1069.227252621.3220975490939318218453.50469098962422028923887.  P90
367     1880785297.14117210027.3570547671926024135523469081.    P102
373     2705777831.2849239123772750489371.      C120
379     6361.14215086019.62792061476751488746157.195266286094155838540091.149039245305638880318701790537479430494077.   P53
383     5407.46274172247987.389804042062703.30384465170048145022609.    P102
389     104707.104718299011.213872651865626627. C126
397     599.132169.     P154
401     4139.3035507.580921563293.      P142
409     35447.1046871190981073158010761424147857.       P129
419     1986323.7107593640109421533.    C144
421     761.192699873029.8881908402042853.      P142
431     234277373353.178545722262071151482152751.       P137
433     1447641166619113176017. C156
439     33073.  P175
443     16054891.       C175
449     1594387.6566983041745360901.    C160
457     4012079.90710124413.563246585673404032021.      P150
461     C191
463     631.647.31536908305027.434131516805761. P159
467     11379319098532079.      C180
479     2609.4481.10627.        C187
487     494441.18299730308381.  C182
491     17929.40163137549.205335958836311.779980872607823.      P160
499     569.9806549.    C197

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