271 (number)

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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
Senary 11316
Octal 4178
Duodecimal 1A712
Hexadecimal 10F16

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]

and .

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]

It is a sexy prime with 277.

Related Research Articles

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<span class="mw-page-title-main">1,000,000,000</span> Natural number

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270 is the natural number following 269 and preceding 271.

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References

  1. ↑ Sloane, N. J. A. (ed.). "SequenceA006512(Greater of twin primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  2. ↑ Sloane, N. J. A. (ed.). "SequenceA002407(Cuban primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  3. ↑ Sloane, N. J. A. (ed.). "SequenceA003215(Hex (or centered hexagonal) numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  4. ↑ Friedman, Erich. "What's Special About This Number?". Archived from the original on 2019-08-25. Retrieved 2018-10-01.
  5. ↑ Sloane, N. J. A. (ed.). "SequenceA154598(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.). "SequenceA066413(Eisenstein-Mersenne primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  7. ↑ Sloane, N. J. A. (ed.). "SequenceA003020(Largest prime factor of the "repunit" number 11...1)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  8. ↑ Sloane, N. J. A. (ed.). "SequenceA061075(Greatest prime number p(n) with decimal fraction period of length n)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
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