Numbers of the form n¹⁵+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 n¹⁵+1 not exceeding m.

E.g. 2¹⁵+1 = 3311331.
So s(2,10) = 3 and s(2,1000) = 3+11+331 = 345.

Also 10¹⁵+1 = 7111321124121619091.
So s(10,100) = 31 and s(10,1000) = 483.

Find ∑ s(n,10⁸) for 1 n 10¹¹.