271 (two hundred
ndseventy-one) is the
natural number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
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 or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime' ...
with
269
Year 269 ( CCLXIX) was a common year starting on Friday of the Julian calendar. At the time, it was known as the Year of the Consulship of Claudius and Paternus (or, less frequently, year 1022 ''Ab urbe condita''). The denomination 269 for this ...
, a
cuban prime (a prime number that is the difference of two consecutive cubes), and a
centered hexagonal number
In mathematics and combinatorics, a centered hexagonal number, or centered hexagon number, is a centered polygonal number, centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot ...
. 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 1 ...
s in the
Eisenstein integer
In mathematics, the Eisenstein integers (named after Gotthold Eisenstein), occasionally also known as Eulerian integers (after Leonhard Euler), are the complex numbers of the form
: z = a + b\omega ,
where and are integers and
: \omega = \frac ...
s.
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 ''Recr ...
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 Multiplication, multiplied by ''x'' yields the multiplicative identity, 1. The multiplicative inverse of a ra ...
is 5:
:
It is a
sexy prime
In number theory, sexy primes are prime numbers that differ from each other by . For example, the numbers and are a pair of sexy primes, because both are prime and 11 - 5 = 6.
The term "sexy prime" is a pun stemming from the Latin word for six ...
with 277.
References
Integers
{{Num-stub