Term

Cuban Prime

Primes of the form 3k²−3k+1 — primes that are also centered hexagonal numbers (7, 19, 37, 61, 127, 271, …).

64 numbers tagged.

A cuban prime is a prime that is the difference of two consecutive cubes: \(p = y^3 - x^3\) with \(y = x+1\), which works out to \(p = 3x^2 + 3x + 1\). The "cuban" refers to cubes, not the country. The sequence: 7, 19, 37, 61, 127, 271, 331, 397, 547, 631, 919.

Neatly, this is exactly the same formula as the [[centered-hexagonal]] numbers, so the cuban primes are precisely the centered hexagonal numbers that happen to be prime. They were named and studied by Allan Cunningham in 1923.

7 19 37 61 127 271 331 397 547 631 919 1,657 1,801 1,951 2,269 2,437 2,791 3,169 3,571 4,219 4,447 5,167 5,419 6,211 7,057 7,351 8,269 9,241 10,267 11,719 12,097 13,267 13,669 16,651 19,441 19,927 22,447 23,497 24,571 25,117 26,227 27,361 33,391 35,317 42,841 45,757 47,251 49,537 50,311 55,897 59,221 60,919 65,269 70,687 73,477 74,419 75,367 81,181 82,171 87,211 88,237 89,269 92,401 96,661

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