Numbers of the form $n^{15}+1$ are composite for every integer $n>1$.
For positive integers $n$ and $m$ let $s(n,m)$ be defined as the sum of the distinct prime factors of $n^{15}+1$ not exceeding $m$.

E.g. $2^{15}+1=3\times 3\times 11\times 331$.
So $s(2,10)=3$ and $s(2,1000)=3+11+331=345$.

Also ${10}^{15}+1=7\times 11\times 13\times 211\times 241\times 2161\times 9091$.
So $s(10,100)=31$ and $s(10,1000)=483$.

Find $\sum s(n,{10}^8)$ for $1\le n\le {10}^{11}$.