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 = 22 + 23 + 24
33 = 32 + 23 + 24
49 = 52 + 23 + 24
47 = 22 + 33 + 24
How many numbers below fifty million can be expressed as the sum of a prime square, prime cube, and prime fourth power?
素数幂三元组
最小的可以表示为一个素数的平方，加上一个素数的立方，再加上一个素数的四次方的数是28。实际上，在小于50的数中，一共有4个数满足这一性质：
28 = 22 + 23 + 24
33 = 32 + 23 + 24
49 = 52 + 23 + 24
47 = 22 + 33 + 24
有多少个小于五千万的数，可以表示为一个素数的平方，加上一个素数的立方，再加上一个素数的四次方？