The first of these equations is
with and . The first few cuban primes from this equation are: 7, 19, 37, 61, 127, 271, 331, 397, 547, 631, 919.
The general cuban prime of this kind can be rewritten as
which simplifies to . This is exactly the general form of a centered hexagonal number; that is, all of these cuban primes are centered hexagonal numbers.
This kind of cuban primes has been researched by A. J. C. Cunningham, in a paper entitled ”On quasi-Mersennian numbers”.
As of January 2006 the largest known cuban prime has 65537 digits with , discovered by Jens Kruse Andersen, according to the Prime Pages of the University of Tennessee at Martin.
The second of these equations is
with . It simplifies to . The first few cuban primes on this form are: 13, 109, 193, 433, 769.
This kind of cuban primes have also been researched by Cunningham, in his book Binomial Factorisations.
The name ”cuban prime” has to do with the rôle cubes (third powers) play in the equations, and has nothing to do with the prime minister of Cuba.
|Date of creation||2013-03-22 16:19:27|
|Last modified on||2013-03-22 16:19:27|
|Last modified by||PrimeFan (13766)|