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A robot is located at the top-left corner of a 64 x 47 grid (marked ‘Start’ in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked ‘Finish’ in the diagram below).

Note: The grid below is 7×3, and is used to illustrate the problem. It is not drawn to scale.

*Image not to scale.

How many possible unique paths are there?

Question:

Find the smallest number that can be expressed as
the sum of 7 consecutive prime numbers,
the sum of 101 consecutive prime numbers,
the sum of 313 consecutive prime numbers,
the sum of 675 consecutive prime numbers,
and is itself a prime number.

For example, 41 is the smallest prime number that can be expressed as
the sum of 3 consecutive primes (11 + 13 + 17 = 41) and
the sum of 6 consecutive primes (2 + 3 + 5 + 7 + 11 + 13 = 41).