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271 (number)

From Wikipedia, the free encyclopedia
Natural number
← 270271 272 →
Cardinaltwo hundred seventy-one
Ordinal271st
(two hundred seventy-first)
Factorizationprime
Primeyes
Greek numeralΣΟΑ´
Roman numeralCCLXXI,cclxxi
Binary1000011112
Ternary1010013
Senary11316
Octal4178
Duodecimal1A712
Hexadecimal10F16

271 (two hundred [and] seventy-one) is thenatural number after270 and before272.

Properties

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271 is atwin prime with269,[1] acuban prime (a prime number that is the difference of two consecutive cubes),[2] and acentered 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=2335{\displaystyle 270=2\cdot 3^{3}\cdot 5} and272=2417{\displaystyle 272=2^{4}\cdot 17}.

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

271 is the largest prime factor of the five-digitrepunit 11111,[7] and the largest prime number for which thedecimal period of itsmultiplicative inverse is 5:[8]

1271=0.00369003690036900369{\displaystyle {\frac {1}{271}}=0.00369003690036900369\ldots }

It is asexy prime with 277.

References

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  1. ^Sloane, N. J. A. (ed.)."Sequence A006512 (Greater of twin primes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^Sloane, N. J. A. (ed.)."Sequence A002407 (Cuban primes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^Sloane, N. J. A. (ed.)."Sequence A003215 (Hex (or centered hexagonal) numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^Friedman, Erich."What's Special About This Number?". Archived fromthe original on 2019-08-25. Retrieved2018-10-01.
  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))".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. ^Sloane, N. J. A. (ed.)."Sequence A066413 (Eisenstein-Mersenne primes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. ^Sloane, N. J. A. (ed.)."Sequence A003020 (Largest prime factor of the "repunit" number 11...1)".TheOn-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)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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