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%I #28 Jun 11 2024 09:44:23
%S 2,4,5,8,9,15,29,213,666,1360,3932,7916
%N Numbers k such that prime(k)^k - primorial(k - 1) is prime.
%C Numbers k such that A304917(k) is prime.
%C a(12) > 4000 if it exists.
%e n = 1 gives 2 - 1 = 1. n=2 gives 3^2 - 2 = 7, so 2 is the first term.
%p N:=2000:
%p for X from 1 to N do
%p Z:=mul(ithprime(i),i=1..(X-1));
%p Y:=(ithprime(X)^X - Z);
%p if isprime(Y) then print(X);
%p end if
%p end do:
%t Select[Range@ 700, PrimeQ[Prime[#]^# - Product[Prime@ i, {i, # - 1}]] &] (* _Michael De Vlieger_, Jul 19 2018 *)
%o (PARI) isok(k) = isprime(prime(k)^k - prod(j=1, k-1, prime(j))); \\ _Michel Marcus_, Jun 09 2018
%Y Cf. A062457, A002110, A304917.
%K nonn,more
%O 1,1
%A _David James Sycamore_, May 24 2018
%E a(12) from _Michael S. Branicky_, Jun 11 2024