# Cuban Primes 1

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:
p=(x^{3}-y^{3})/(x-y), x=y+1, y>0

The general cuban prime of this kind can be rewritten as ((y+1)^{3}-y^{3})/(y+1-y) which simplifies to 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.

First 20: 7, 19, 37, 61, 127, 271, 331, 397, 547, 631, 919, 1657, 1801, 1951, 2269, 2437, 2791, 3169, 3571, 4219

Checkout list of first: 10, 50, 100, 500 Cuban primes 1. You can also check all Cuban primes 1.

## External#

- OEIS: A002407
- Wikipedia: Cuban Primes

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