## Smallest prime factor

### Problem 521

Let smpf(`n`) be the smallest prime factor of `n`.

smpf(91)=7 because 91=7×13 and smpf(45)=3 because 45=3×3×5.

Let S(`n`) be the sum of smpf(`i`) for 2 ≤ `i` ≤ `n`.

E.g. S(100)=1257.

Find S(10^{12}) mod 10^{9}.