0%

Problem 87


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?