A057017 Numbers k such that the product of the first k composite numbers minus 1 is a prime.

1, 2, 3, 9, 12, 22, 26, 30, 34, 51, 54, 100, 125, 155, 168, 173, 220, 401, 494, 2161, 2539, 2866, 7625, 9644, 12099, 13470, 16078, 18587, 30075, 37067

Offset: 1

Author

Robert G. Wilson v, Apr 21 2001

Keywords

• nonn

Examples

			a(3) = 3 because 4*6*8-1 = 191 which is prime.
		

Crossrefs

Cf. A049421, A053982, A140293.

Programs

Mathematica

Composite[ n_Integer ] := (k = n + PrimePi[ n ] + 1; While[ k - PrimePi[ k ] - 1 != n, k++ ]; k); Do[ m = n; If[ PrimeQ[ Product[ Composite[ k ], {k, 1, n} ] - 1 ], Print[ n ] ], {n, 1, 1980} ]

Extensions

More terms via A049421 from Jeppe Stig Nielsen, Aug 12 2024