0,1

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.

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).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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

(0!+1)=[2], (1!+1)=[2], (2!+1)=[3], (3!+1)=[7], (4!+1)=25=5*[5], (5!+1)=121=11*[11], (6!+1)=721=7*[103], (7!+1)=5041=71*[71], etc. - Mitch Cervinka (puritan(AT)toast.net), May 11 2009

PrimeFactors[n_]:=Flatten[Table[ #[[1]], {1}]&/@FactorInteger[n]]; Table[PrimeFactors[n!+1][[ -1]], {n, 0, 35}] ..and/or.. Table[FactorInteger[n!+1, FactorComplete->True][[ -1, 1]], {n, 0, 35}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 12 2009]

Cf. A002582, A038507, A051301, A056111, A096225.

Sequence in context: A134232 A123934 A051301 this_sequence A068519 A083702 A108041

Adjacent sequences: A002580 A002581 A002582 this_sequence A002584 A002585 A002586

nonn,nice,easy

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 01 2000. Corrected by Jud McCranie (j.mccranie(AT)comcast.net), Jan 03 2001.