271 (number)

271 is a twin prime with 269,^[1] a cuban prime (a prime number that is the difference of two consecutive cubes),^[2] and a centered hexagonal number.^[3] It is the smallest prime number bracketed on both sides by numbers divisible by cubes,^[4] and the smallest prime number bracketed by numbers with five primes (counting repetitions) in their factorizations:^[5]

${\displaystyle 270=2\cdot 3^{3}\cdot 5}$ and ${\displaystyle 272=2^{4}\cdot 17}$.

After 7, 271 is the second-smallest Eisenstein–Mersenne prime, one of the analogues of the Mersenne primes in the Eisenstein integers.^[6]

271 is the largest prime factor of the five-digit repunit 11111,^[7] and the largest prime number for which the decimal period of its multiplicative inverse is 5:^[8]

${\displaystyle {\frac {1}{271}}=0.00369003690036900369\ldots }$

It is a sexy prime with 277.