data/problems/131.yml
---
:id: 131
:name: Prime cube partnership
:url: https://projecteuler.net/problem=131
:content: |+
There are some prime values, _p_, for which there exists a positive integer, _n_, such that the expression _n_<sup>3</sup> + _n_<sup>2</sup>_p_ is a perfect cube.
For example, when _p_ = 19, 8<sup>3</sup> + 8<sup>2</sup>×19 = 12<sup>3</sup>.
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?