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

Author

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

Keywords

• nonn

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.

Examples

			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.
		

Crossrefs

Cf. A083520, A083522.

Programs

PARI

m=1000; for(n=1,18,b=0; k=1; while(b<1&&k
				

Extensions

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