Cuban prime

A cuban prime (from the role cubes (third powers) play in the equations) is a prime number that is a solution to one of two different specific equations involving third powers of x and y. The first of these equations is:

and the first few cuban primes from this equation are:

7, 19, 37, 61, 127, 271, 331, 397, 547, 631, 919, 1657, 1801, 1951, 2269, 2437, 2791, 3169, 3571, 4219, 4447, 5167, 5419, 6211, 7057, 7351, 8269, 9241, ... (sequence in the OEIS)

The general cuban prime of this kind can be rewritten as ${\displaystyle {\tfrac {(y+1)^{3}-y^{3}}{y+1-y}}}$, which simplifies to ${\displaystyle 3y^{2}+3y+1}$. This is exactly the general form of a centered hexagonal number; that is, all of these cuban primes are centered hexagonal.

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Wikipedia