271 (number)

Short description: Natural number

| <- 270  | 271 |  272 ->

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← 200 210 220 230 240 250 260 270 280 290 →

List of numbers — Integers

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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
Quaternary| 100334
Quinary| 20415
Senary| 11316
Octal| 4178
Duodecimal| 1A712
Hexadecimal| 10F16
Vigesimal| DB20
Base 36| 7J36

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]

[math]\displaystyle{ 270=2\cdot 3^3\cdot 5 }[/math] and [math]\displaystyle{ 272=2^4\cdot 17 }[/math].

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]

[math]\displaystyle{ \frac{1}{271}=0.00369003690036900369\ldots }[/math]

It is a sexy prime with 277.

## References

1. ↑ Sloane, N. J. A., ed. "Sequence A006512 (Greater of twin primes)". OEIS Foundation. https://oeis.org/A006512.
2. ↑ Sloane, N. J. A., ed. "Sequence A002407 (Cuban primes)". OEIS Foundation. https://oeis.org/A002407.
3. ↑ Sloane, N. J. A., ed. "Sequence A003215 (Hex (or centered hexagonal) numbers)". OEIS Foundation. https://oeis.org/A003215.
4. ↑ Friedman, Erich. "What's Special About This Number?". 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))". OEIS Foundation. https://oeis.org/A154598.
6. ↑ Sloane, N. J. A., ed. "Sequence A066413 (Eisenstein-Mersenne primes)". OEIS Foundation. https://oeis.org/A066413.
7. ↑ Sloane, N. J. A., ed. "Sequence A003020 (Largest prime factor of the "repunit" number 11...1)". OEIS Foundation. https://oeis.org/A003020.
8. ↑ Sloane, N. J. A., ed. "Sequence A061075 (Greatest prime number p(n) with decimal fraction period of length n)". OEIS Foundation. https://oeis.org/A061075.

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