A064998 a(n) is the smallest prime p such that p*n! +- 1 are twin primes.

2, 2, 3, 2, 17, 7, 7, 3, 61, 29, 167, 401, 167, 19, 311, 461, 97, 919, 47, 71, 1483, 107, 13, 1571, 821, 1361, 769, 239, 163, 4229, 593, 373, 1571, 173, 6229, 3331, 1879, 2837, 2633, 12329, 2311, 269, 4159, 1217, 9719, 509, 3049, 8429, 307, 6121, 7919

Offset: 2

Author

Robert G. Wilson v, Oct 31 2001

Keywords

• nonn

Examples

			a(6) = 17 because 17*6! = 12240, 12240 + 1 and 12240 - 1 are twin primes, and there is no prime less than 17 for which this pairing will work.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 2..200

Crossrefs

Cf. A051888, A064983.

Programs

Mathematica

Do[k = 1; While[ !PrimeQ[ Prime[k]*n! - 1] || !PrimeQ[ Prime[k]*n! + 1], k++ ]; Print[ Prime[k]], {n, 2, 75} ]

PARI

{ allocatemem(932245000); for (n=2, 200, f=n!; p=2; while (!isprime(p*f + 1) || !isprime(p*f - 1), p=nextprime(p + 1)); write("b064998.txt", n, " ", p) ) } \\ Harry J. Smith, Oct 03 2009