

A103319


Primes of the form p! + 1 where p is prime.


2



3, 7, 39916801, 13763753091226345046315979581580902400000001, 33452526613163807108170062053440751665152000000001, 4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000001
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OFFSET

1,1


COMMENTS

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).


REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, Section A2.


LINKS

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 BC2012) 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.


EXAMPLE

2 and 2! + 1 = 3 are prime, so 3 is a member.


MATHEMATICA

Select[Table[p!+1, {p, Prime[Range[30]]}], PrimeQ] (* Harvey P. Dale, Nov 28 2019 *)


CROSSREFS

Cf. A093804, A002981, A088332, A103318.
Sequence in context: A137029 A174307 A137125 * A153021 A155979 A120669
Adjacent sequences: A103316 A103317 A103318 * A103320 A103321 A103322


KEYWORD

hard,nonn


AUTHOR

Jonathan Sondow, Jan 31 2005


STATUS

approved



