OFFSET
1,1
COMMENTS
f(89) is a 131-digit prime.
According to Wilson's theorem, f(q) can be an integer only if q is prime.
MATHEMATICA
Select[Prime[Range[100]], PrimeQ[((((# - 1)! + 1) / #) + 1) / (# + 1)] &] (* Vincenzo Librandi, Sep 21 2018 *)
PROG
(PARI) forprime(q=7, 89, my(p = ((((q - 1)! + 1) / q) + 1) / (q + 1)); if(ispseudoprime(p), print1(q, ", ")))
(Magma) [n: n in [1..100] | IsPrime(n) and IsPrime((((Factorial(n-1)+1) div n)+1) div (n+1))]; // Vincenzo Librandi, Sep 21 2018
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Rashid Naimi, Sep 16 2018
EXTENSIONS
1621 and 1699, which do not belong here, removed by Rashid Naimi, Mar 21 2019
STATUS
approved