Problem 320

Factorials divisible by a huge integer

Published on Saturday, 15th January 2011, 10:00 pm; Solved by 440

Let N(i) be the smallest integer n such that n! is divisible by (i!)^1234567890

Let S(u)=N(i) for 10 i u.

S(1000)=614538266565663.

Find S(1 000 000) mod 10¹⁸.