For any prime $p$ the number $N(p,q)$ is defined by $N(p,q)=\sum _{n=0}^q{T}_n\cdot p^n$
with $T_n$ generated by the following random number generator:

$S_0=290797$
$S_{n+1}=S_n^{2}mod50515093$
$T_n=S_{n}modp$

Let $\mathrm{Nfac}(p,q)$ be the factorial of $N(p,q)$.
Let $\mathrm{NF}(p,q)$ be the number of factors $p$ in $\mathrm{Nfac}(p,q)$.

You are given that $\mathrm{NF}(3,10000)mod{3}^{20}=624955285$.

Find $\mathrm{NF}(61,{10}^7)mod{61}^{10}$.