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A huge binomial coefficient

Problem 365

Published on Saturday, 31st December 2011, 04:00 pm; Solved by 756; Difficulty rating: 40%

The binomial coefficient C(1018,109) is a number with more than 9 billion (9×109) digits.

Let M(n,k,m) denote the binomial coefficient C(n,k) modulo m.

Calculate ∑M(1018,109,p*q*r) for 1000<p<q<r<5000 and p,q,r prime.