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Old 2018-06-01, 17:51   #89
sweety439
 
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........
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Old 2018-06-01, 17:54   #90
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Extended to n=512, since the smallest number such that the program cannot compute the full fraction is n=526. (see http://oeis.org/A003285 for the period length, the period length for n=1 to n=64 are 0, 1, 2, 0, 1, 2, 4, 2, 0, 1, 2, 2, 5, 4, 2, 0, 1, 2, 6, 2, 6, 6, 4, 2, 0, 1, 2, 4, 5, 2, 8, 4, 4, 4, 2, 0, 1, 2, 2, 2, 3, 2, 10, 8, 6, 12, 4, 2, 0, 1, 2, 6, 5, 6, 4, 2, 6, 7, 6, 4, 11, 4, 2, 0)
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Last fiddled with by sweety439 on 2018-06-01 at 18:03
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Old 2018-06-01, 21:34   #91
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Old 2018-06-01, 21:53   #92
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Old 2018-06-01, 22:45   #93
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Format:

[prime, period]: smallest base
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Old 2018-06-01, 23:31   #94
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..............
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Old 2018-06-13, 17:41   #95
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.........
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Old 2018-06-19, 19:21   #96
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Relative class number h- of cyclotomic field Q(zeta_n) for n up to 256. (only n<=236 have been doublechecked, thus there may be error for n>236)
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Old 2018-07-01, 13:05   #97
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..
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Old 2018-07-10, 23:14   #98
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search limit: 2048 for n<=133, 1024 for n>=134
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Old 2018-07-11, 23:30   #99
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range: 1<=k<=n-2 (we do not include k=n-1)

conjectures:

0 only for n = 1, 2, 3
1 only for n = 23, 52
2 only for n = 4, 5, 7, 11
3 only for n = 6, 19, 26, 40, 59, 97, 105, 247, 266
4 only for 8, 9, 10, 13, 14, 16, 22, 25, 37, 41, 54, 70, 76, 110, 119, 141, 142, 189

and for every r, there is an n such that a(k)>r for all k>n.
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File Type: txt primes of the form phi(k,n-k).txt (22.5 KB, 130 views)
File Type: txt number of primes of the form phi(k,n-k).txt (1.7 KB, 31 views)

Last fiddled with by sweety439 on 2018-07-11 at 23:39
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