271 (number)

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

Properties

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]

[math]\displaystyle{ 270=2\cdot 3^3\cdot 5 }[/math] and [math]\displaystyle{ 272=2^4\cdot 17 }[/math].

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]

[math]\displaystyle{ \frac{1}{271}=0.00369003690036900369\ldots }[/math]

It is a sexy prime with 277.

References

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