题目131：求使得n^3 + n^2 * p为完全立方数的质数p

欧拉计划

Prime cube partnership

There are some prime values, p, for which there exists a positive integer, n, such that the expression n³ + n²p is a perfect cube.

For example, when p = 19, 8³ + 8²×19 = 12³.

What is perhaps most surprising is that for each prime with this property the value of n is unique, and there are only four such primes below one-hundred.

How many primes below one million have this remarkable property?

题目：

对于某些质数 p，存在一个正整数 n，使得 n³ + n²p 是完全立方数。

例如，当 p=19 时，8³ + 8²×19 = 12³.

令人惊奇的是，对于每个具有上述性质的质数 p，对应的 n 是唯一的，而且 100 以下只有 4 个这样的质数。

一百万以下有多少质数具有上述性质？