Problem 288
An enormous factorial

For any prime p the number N(p,q) is defined by N(p,q) = ∑n=0 to q Tn*pn
with Tn generated by the following random number generator:

S0 = 290797
Sn+1 = Sn2 mod 50515093
Tn = Sn mod p

Let Nfac(p,q) be the factorial of N(p,q).
Let NF(p,q) be the number of factors p in Nfac(p,q).

You are given that NF(3,10000) mod 320=624955285.

Find NF(61,107) mod 6110

These problems are part of Project Euler and are licensed under CC BY-NC-SA 2.0 UK