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: 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, 10267, 11719, 12097, 13267, 13669, 16651, 19441, 19927, 22447, 23497, 24571, 25117, 26227 The general cuban prime of this kind can be rewritten as ((y+1)3 - y3) / (y + 1 - y), which simplifies to 3y2 + 3y + 1. This is exactly the general form of a Centered Hexagonal Number ; that is, all of these cuban primes are centered hexagonal. 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 has 65537 digits with y = 1000008454096 {Link without Title} , found by Jens Kruse Andersen. The second of these equations is: : It simplifies to 3y2 + 6y + 4. The first few cuban primes on this form are: 13 , 109 , 193, 433, 769, 1201, 1453, 2029, 3469, 3889, 4801, 10093, 12289, 13873, 18253, 20173, 21169, 22189, 28813, 37633, 43201, 47629, 60493, 63949, 65713, 69313 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 role cubes (third powers) play in the equations, and has nothing to do with . |
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