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Search: id:A051301
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| A051301 |
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Smallest prime factor of n!+1. |
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+0
8
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| 2, 2, 3, 7, 5, 11, 7, 71, 61, 19, 11, 39916801, 13, 83, 23, 59, 17, 661, 19, 71, 20639383, 43, 23, 47, 811, 401, 1697, 10888869450418352160768000001, 29, 14557, 31, 257, 2281, 67, 67411, 137, 37, 13763753091226345046315979581580902400000001
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Theorem: For any N, there is a prime > N. Proof: Consider any prime factor of N!+1.
Cf. Wilson's Theorem (1770): p | (p-1)! + 1 iff p is a prime.
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REFERENCES
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Albert H. Beiler, "Recreations in The Theory of Numbers, The Queen of Mathematics Entertains," Dover Publ. NY, 1966, Page 49.
A. Borning, Some results for k!+-1 and 2.3.5...p+-1, Math. Comp., 26 (1972), 567-570.
M. Kraitchik, On the divisibility of factorials, Scripta Math., 14 (1948), 24-26 (but beware errors).
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100 (derived from Hisanori Mishima's data)
Hisanori Mishima, Factorizations of many number sequences
Hisanori Mishima, Factorizations of many number sequences
R. G. Wilson v, Explicit factorizations
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MAPLE
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with(numtheory); A051301 := n->divisors(n)[2];
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MATHEMATICA
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Do[ Print[ FactorInteger[ n! + 1, FactorComplete -> True ] [ [ 1, 1 ] ] ], {n, 0, 38} ]
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CROSSREFS
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Cf. A002583, A038507, A096225.
Sequence in context: A021451 A134232 A123934 this_sequence A002583 A068519 A083702
Adjacent sequences: A051298 A051299 A051300 this_sequence A051302 A051303 A051304
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KEYWORD
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nonn,easy
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu)
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