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271 (number)
Natural number

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

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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

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.

References

  1. Sloane, N. J. A. (ed.). "Sequence A006512 (Greater of twin primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. /wiki/Neil_Sloane ↩

  2. Sloane, N. J. A. (ed.). "Sequence A002407 (Cuban primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. /wiki/Neil_Sloane ↩

  3. Sloane, N. J. A. (ed.). "Sequence A003215 (Hex (or centered hexagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. /wiki/Neil_Sloane ↩

  4. Friedman, Erich. "What's Special About This Number?". Archived from the original on 2019-08-25. Retrieved 2018-10-01. https://web.archive.org/web/20190825183505/https://www2.stetson.edu/~efriedma/numbers.html ↩

  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. /wiki/Neil_Sloane ↩

  6. Sloane, N. J. A. (ed.). "Sequence A066413 (Eisenstein-Mersenne primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. /wiki/Neil_Sloane ↩

  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. /wiki/Neil_Sloane ↩

  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. /wiki/Neil_Sloane ↩