The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. Find the sum of all the primes below two million.
A Pythagorean triplet is a set of three natural numbers, a < b < c, for which, a^(2) + b^(2) = c^(2) For example, 3^(2) + 4^(2) = 9 + 16 = 25 = 5^(2). There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc.
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