Problem 249

Prime Subset Sums

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.

**
These problems are part of
Project Euler
and are licensed under
CC BY-NC-SA 2.0 UK
**