271 (two hundred
ndseventy-one) is the
natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called ''cardinal ...
after and before .
Properties
271 is a
twin prime
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin p ...
with
269
Year 269 (Roman numerals, CCLXIX) was a common year starting on Friday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Claudius and Paternus (or, less frequently, year 102 ...
, a
cuban prime
A cuban prime is a prime number that is also a solution to one of two different specific equations involving differences between third powers of two integers ''x'' and ''y''.
First series
This is the first of these equations:
:p = \frac,\ x = ...
(a prime number that is the difference of two consecutive cubes), and a
centered hexagonal number. It is the smallest prime number bracketed on both sides by numbers divisible by cubes, and the smallest prime number bracketed by numbers with five primes (counting repetitions) in their factorizations:
:
and
.
After 7, 271 is the second-smallest Eisenstein–Mersenne prime, one of the analogues of the
Mersenne prime
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th ...
s in the
Eisenstein integers.
271 is the largest prime factor of the five-digit
repunit
In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1 — a more specific type of repdigit. The term stands for repeated unit and was coined in 1966 by Albert H. Beiler in his book ''Recreat ...
11111, and the largest prime number for which the
decimal period of its
multiplicative inverse
In mathematics, a multiplicative inverse or reciprocal for a number ''x'', denoted by 1/''x'' or ''x''−1, is a number which when multiplied by ''x'' yields the multiplicative identity, 1. The multiplicative inverse of a fraction ''a''/ ...
is 5:
:
It is a
sexy prime
In number theory, sexy primes are prime numbers that differ from each other by 6. For example, the numbers 5 and 11 are both sexy primes, because both are prime and .
The term "sexy prime" is a pun stemming from the Latin word for six: .
If o ...
with 277.
References
{{Integers, 2
Integers