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A103319
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Primes of the form p! + 1 where p is prime.
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2
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3, 7, 39916801, 13763753091226345046315979581580902400000001, 33452526613163807108170062053440751665152000000001, 4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000001
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OFFSET
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1,1
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COMMENTS
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The values of p are 2, 3, 11, 37, 41, 73 which is A093804 (with a different definition). Subsequence of A088332 (primes of the form n! + 1).
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, Section A2.
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LINKS
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Table of n, a(n) for n=1..6.
R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670, 2012 - From N. J. A. Sloane, Jun 13 2012
Eric Weisstein's World of Mathematics, Factorial Prime
Index entries for sequences related to factorial numbers.
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EXAMPLE
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2 and 2! + 1 = 3 are prime, so 3 is a member.
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MATHEMATICA
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Select[Table[p!+1, {p, Prime[Range[30]]}], PrimeQ] (* Harvey P. Dale, Nov 28 2019 *)
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CROSSREFS
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Cf. A093804, A002981, A088332, A103318.
Sequence in context: A137029 A174307 A137125 * A153021 A155979 A120669
Adjacent sequences: A103316 A103317 A103318 * A103320 A103321 A103322
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KEYWORD
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hard,nonn
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AUTHOR
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Jonathan Sondow, Jan 31 2005
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STATUS
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approved
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