OFFSET
1,1
COMMENTS
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.)
Observe that a(2) = 31 = 2*3 + 5^2 = 2*3*5 + 1, so it has two "primorial forms".
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..100
EXAMPLE
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.
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, May 04 2000
EXTENSIONS
Edited by Jon E. Schoenfield, May 22 2018
More terms from Michael De Vlieger, May 22 2018
STATUS
approved