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Participate: 
The semiprime 4031 is the sum of the cubes of the first 6
primes: 2^3 + 3^3 + 5^3 + 7^3 + 11^3 + 13^3 = 4031 = 29 *
139. Curiously, it shares a prime factor with the sum of
the squares of the first 6 primes. 2^2 + 3^2 + 5^2 + 7^2 +
11^2 + 13^2 = 377 = 13 * 29. [Post]
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