There are two primes, both below 100, that evenly divide the sum of the primes less than themselves.

Find those two primes.

The only other such prime below 2,000,000 is M, the n-th prime.

Find M and n.

(In reply to computer solution by Charlie)

A search for 369119 in Sloane's OEIS finds that the next such prime is 415074643, which is the 22096548th prime, and no others exist below 10^12.

BTW, Sloane does list 2 among these primes.

Edited on February 12, 2012, 6:36 pm

Posted by Charlie on 2012-02-12 18:33:42