A cuban prime 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 (sequence A002407 in OEIS):
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, which simplifies to . This is exactly the general form of a centered hexagonal number; that is, all of these cuban primes are centered hexagonal.
As of January 2006 the largest known has 65537 digits with, found by Jens Kruse Andersen.
The second of these equations is:
It simplifies to . The first few cuban primes on this form are (sequence A002648 in OEIS):
- 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
The name "cuban prime" has to do with the role cubes (third powers) play in the equations, and has nothing to do with Cuba.
Famous quotes containing the words cuban and/or prime:
“Because a person is born the subject of a given state, you deny the sovereignty of the people? How about the child of Cuban slaves who is born a slave, is that an argument for slavery? The one is a fact as well as the other. Why then, if you use legal arguments in the one case, you don’t in the other?”
—Franz Grillparzer (1791–1872)
“My prime of youth is but a frost of cares,
My feast of joy is but a dish of pain,
My crop of corn is but a field of tares,
And all my good is but vain hope of gain:
The day is past, and yet I saw no sun,
And now I live, and now my life is done.”
—Chidiock Tichborne (1558–1586)