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Prime Subset Sums

Problem 249

Published on Saturday, 13th June 2009, 05:00 am; Solved by 1562

Let S = {2, 3, 5, ..., 4999} be the set of prime numbers less than 5000.

Find the number of subsets of S, the sum of whose elements is a prime number.
Enter the rightmost 16 digits as your answer.