A083521 Smallest prime that is the product of n consecutive integers + 1, or 0 if no such number exists.

2, 3, 7, 0, 2521, 20161, 604801, 6652801, 726485761, 39916801, 39916801, 140792940288001, 14820309504001, 10461394944001, 641171050071552001, 425757851430912001, 9366672731480064001, 8515157028618240001

Offset

0,1

Comments

The product of four consecutive integers + 1 is always composite (a square), so a(4) = 0. Are there any more zeros in the sequence?

The Pocklington-Lehmer "P-1" primality test is used, as implemented in PARI 2.1.3.

Links

Table of n, a(n) for n=0..17.

Example

1*2*3*4*5 + 1 = 121 = 11*11 and 2*3*4*5*6 + 1 = 721 = 7*103 are composite, but 3*4*5*6*7 + 1 = 2521 is prime, so a(5) = 2521.

Prog

(PARI) m=1000; for(n=1, 18, b=0; k=1; while(b<1&&k<m, if(!isprime(p=prod(j=k, k+n-1, j)+1, 1), k++, b=1)); print1(if(k<m, p, 0), ", "))

Crossrefs

Cf. A083520, A083522.

Sequence in context: A249523 A301316 A023048 * A104691 A011160 A068960

Adjacent sequences: A083518 A083519 A083520 * A083522 A083523 A083524

Keyword

nonn

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 05 2003

Extensions

Edited and extended by Klaus Brockhaus and Don Reble, May 06 2003

Status

approved