A065314 Smallest prime divisor of (n-th primorial - (n+1)-st prime).

23, 199, 2297, 30013, 41, 9699667, 2819, 53, 21701, 79, 163, 181, 61, 1619, 14669, 307, 103, 306091, 907, 3217644767340672907899084554047, 267064515689275851355624017992701, 23768741896345550770650537601358213

Offset: 3

Author

Labos Elemer, Oct 29 2001

Keywords

• nonn

Examples

			For n=3, 3rd primorial=30, prime(4)=7, difference=23, so a(3)=23.
		

Links

• Tyler Busby, Table of n, a(n) for n = 3..104 (terms 3..40 from Michel Marcus, terms 41..80 from Sean A. Irvine)
• Romeo 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 [math.HO], 2012-2023. - _N. J. A. Sloane_, Jun 13 2012

Crossrefs

Cf. A002110, A000040, A006530, A006530, A057713, A002584, A002585, A051342.

Cf. A065315, A065316, A065317.

Programs

Mathematica

Map[FactorInteger[Times @@ #1 - #2][[1, 1, 1]] & @@ Reverse@ TakeDrop[#, -1] &, Drop[#, 3] &@ FoldList[Flatten@ Append[{#1}, #2] &, Prime@ Range@ 25]] (* Michael De Vlieger, Jul 16 2017 *)

PARI

a(n) = vecmin(factor(prod(k=1, n, prime(k)) - prime(n+1))[,1]); \\ Michel Marcus, Jul 16 2017

Formula

a(n) = A020639( A002110(n) - A000040(n+1) ).