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%I #18 May 26 2018 11:20:56
%S 11,31,79,331,2531,30319,511039,9700357,223093769,6469694377,
%T 200560491721,7420738136831,304250263529059,13082761331672803,
%U 614889782588494961,32589158477190048817,1922760350154212643889,117288381359406970988027,7858321551080267055884131,557940830126698960967422909
%N a(n) is the smallest prime of the form Q + c, where Q is the n-th primorial and c is a composite >= prime(n+1)^2.
%C Between 2310 and 2531 there are 26 primes (2311, ..., 2521), all of which are of the form (primorial + prime). (2311 = 2 + 2309 (prime) = 2*3*5 + 2281 (prime); each of the other 25 primes is of the form 2*3*5*7*11 + prime.)
%C Observe that a(2) = 31 = 2*3 + 5^2 = 2*3*5 + 1, so it has two "primorial forms".
%H Michael De Vlieger, <a href="/A038773/b038773.txt">Table of n, a(n) for n = 1..100</a>
%e At n=5, the 5th primorial is A002110(5)=2310 and 2310 + 13*17 = 2310 + 221 = 2531 is the prime that meets the criteria of the definition.
%t Array[Block[{Q = Product[Prime@ i, {i, #}], c = Prime[# + 1]^2}, While[Nand[PrimeQ[Q + c], CompositeQ@ c], c++]; Q + c] &, 17] (* _Michael De Vlieger_, May 22 2018 *)
%o (PARI) a(n) = {my(pr = prod(k=1, n, prime(k)), c = prime(n+1)^2); while (isprime(c) || !isprime(pr + c), c++); pr + c;} \\ _Michel Marcus_, May 26 2018
%Y Cf. A002110, A054757, A054758, A005235.
%K nonn
%O 1,1
%A _Labos Elemer_, May 04 2000
%E Edited by _Jon E. Schoenfield_, May 22 2018
%E More terms from _Michael De Vlieger_, May 22 2018
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