131 Prime cube partnership.sf

#!/usr/bin/ruby

# Author: Daniel "Trizen" Șuteu
# License: GPLv3
# Website: https://github.com/trizen

# General formula: n^9 + n^6 * p = (n^3 + n^2)^3 where p is a prime number.
# From the above formula results that p must have the form: 3n^2 + 3n + 1.

# https://projecteuler.net/problem=131

# Runtime: 0.110s

var count = 0

for (var n = 1; true ; ++n) {
    var p = (3*n**2 + 3*n + 1)
    p < 1e6 || break
    p.is_prime && ++count
}

say count