271 (number)

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

← 270 271 272 →
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Cardinal	two hundred seventy-one
Ordinal	271st (two hundred seventy-first)
Factorization	prime
Prime	yes
Greek numeral	ΣΟΑ´
Roman numeral	CCLXXI
Binary	1000011112
Ternary	1010013
Octal	4178
Duodecimal	1A712
Hexadecimal	10F16

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]

${\displaystyle 270=2\cdot 3^{3}\cdot 5}$ 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.

References

1. Sloane, N. J. A. (ed.). "Sequence A006512 (Greater of twin primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
2. Sloane, N. J. A. (ed.). "Sequence A002407 (Cuban primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
3. Sloane, N. J. A. (ed.). "Sequence A003215 (Hex (or centered hexagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
4. Friedman, Erich. "What's Special About This Number?". Retrieved 2018-10-01.
5. Sloane, N. J. A. (ed.). "Sequence A154598 (a(n) is the smallest prime p such that p-1 and p+1 both have n prime factors (with multiplicity))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
6. Sloane, N. J. A. (ed.). "Sequence A066413 (Eisenstein-Mersenne primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
7. Sloane, N. J. A. (ed.). "Sequence A003020 (Largest prime factor of the "repunit" number 11...1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
8. Sloane, N. J. A. (ed.). "Sequence A061075 (Greatest prime number p(n) with decimal fraction period of length n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.