Programming Praxis

This puzzle comes from the 2008 Google Treasure Hunt:

Find the smallest number that can be expressed as the sum of 7 consecutive prime numbers, the sum of 17 consecutive prime numbers, the sum of 41 consecutive prime numbers, the sum of 541 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).

Your task is to find the number. When you are finished, you can read or run a suggested solution, or post your solution or discuss the exercise in the comments below.

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