Problem 131
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?
素数立方数组合
对于某些素数p，存在正整数n，使得表达式n3 + n2p是立方数。
例如，对于p = 19，83 + 82×19 = 123。
非常奇特的是，对于满足这个性质的素数，n的值都是唯一的。在小于一百的素数中，只有四个素数满足这个性质。
在小于一百万的素数中，有多少个素数满足这个神奇的性质？