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%I #7 Oct 19 2017 03:14:16
%S 2,3,7,0,2521,20161,604801,6652801,726485761,39916801,39916801,
%T 140792940288001,14820309504001,10461394944001,641171050071552001,
%U 425757851430912001,9366672731480064001,8515157028618240001
%N Smallest prime that is the product of n consecutive integers + 1, or 0 if no such number exists.
%C The product of four consecutive integers + 1 is always composite (a square), so a(4) = 0. Are there any more zeros in the sequence?
%C The Pocklington-Lehmer "P-1" primality test is used, as implemented in PARI 2.1.3.
%e 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.
%o (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),","))
%Y Cf. A083520, A083522.
%K nonn
%O 0,1
%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 05 2003
%E Edited and extended by _Klaus Brockhaus_ and _Don Reble_, May 06 2003
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