# 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?