| ||||
|---|---|---|---|---|
| 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.
References
- ^ Sloane, N. J. A. (ed.). "Sequence A006512 (Greater of twin primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002407 (Cuban primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A003215 (Hex (or centered hexagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Friedman, Erich. "What's Special About This Number?". Archived from the original on 2019-08-25. Retrieved 2018-10-01.
- ^ 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A066413 (Eisenstein-Mersenne primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.
- ^ 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.