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271 (number) - Wikipedia

From Wikipedia, the free encyclopedia

Natural number

271 (two hundred [and] seventy-one) is the natural number after 270 and before 272.

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]

270 = 2 ⋅ 3 3 ⋅ 5 {\displaystyle 270=2\cdot 3^{3}\cdot 5} and 272 = 2 4 ⋅ 17 {\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]

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

It is a sexy prime with 277.

Integers −1 0s 100s 200s 300s 400s 500s 600s 700s 800s 900s 1000s

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