271 (number)
| ||||
|---|---|---|---|---|
| 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
- ↑ Sloane, N. J. A., ed. "Sequence A006512 (Greater of twin primes)". OEIS Foundation. https://oeis.org/A006512.
- ↑ Sloane, N. J. A., ed. "Sequence A002407 (Cuban primes)". OEIS Foundation. https://oeis.org/A002407.
- ↑ Sloane, N. J. A., ed. "Sequence A003215 (Hex (or centered hexagonal) numbers)". OEIS Foundation. https://oeis.org/A003215.
- ↑ Friedman, Erich. "What's Special About This Number?". https://www2.stetson.edu/~efriedma/numbers.html.
- ↑ 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.
- ↑ Sloane, N. J. A., ed. "Sequence A066413 (Eisenstein-Mersenne primes)". OEIS Foundation. https://oeis.org/A066413.
- ↑ Sloane, N. J. A., ed. "Sequence A003020 (Largest prime factor of the "repunit" number 11...1)". OEIS Foundation. https://oeis.org/A003020.
- ↑ 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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