Problem 87

Prime power triples

The smallest number expressible as the sum of a prime square, prime cube, and prime fourth power is 28. In fact, there are exactly four numbers below fifty that can be expressed in such a way:

28 = 2^{2} + 2^{3} + 2^{4}

33 = 3^{2} + 2^{3} + 2^{4}

49 = 5^{2} + 2^{3} + 2^{4}

47 = 2^{2} + 3^{3} + 2^{4}

How many numbers below fifty million can be expressed as the sum of a prime square, prime cube, and prime fourth power?

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These problems are part of
Project Euler
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