257 (two hundred
ndfifty-seven) is the natural number following
256 and preceding
258.
In mathematics
257 is a
prime number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
of the form
specifically with ''n'' = 3, and therefore a
Fermat prime
In mathematics, a Fermat number, named after Pierre de Fermat, who first studied them, is a positive integer of the form
:F_ = 2^ + 1,
where ''n'' is a non-negative integer. The first few Fermat numbers are:
: 3, 5, 17, 257, 65537, 4294967 ...
. Thus a
regular polygon with 257 sides is
constructible with compass and unmarked straightedge. It is currently the second largest known Fermat prime.
Analogously, 257 is the third
Sierpinski prime of the first kind, of the form
➜
.
It is also
a
balanced prime In number theory, a balanced prime is a prime number with equal-sized prime gaps above and below it, so that it is equal to the arithmetic mean of the nearest primes above and below. Or to put it algebraically, given a prime number p_n, where is it ...
,
an
irregular prime
In number theory, a regular prime is a special kind of prime number, defined by Ernst Kummer in 1850 to prove certain cases of Fermat's Last Theorem. Regular primes may be defined via the divisibility of either class numbers or of Bernoulli num ...
,
a prime that is one more than a square,
and a
Jacobsthal–Lucas number In mathematics, the Jacobsthal numbers are an integer sequence named after the German mathematician Ernst Jacobsthal. Like the related Fibonacci numbers, they are a specific type of Lucas sequence U_n(P,Q) for which ''P'' = 1, and ''Q' ...
.
There are exactly 257 combinatorially distinct
convex polyhedra
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the n-dimensional Euclidean space \mathbb^n. Most texts. use the term "polytope" for a bounded convex polytope, and the wo ...
with eight
vertices (or
polyhedral graph
In geometric graph theory, a branch of mathematics, a polyhedral graph is the undirected graph formed from the vertices and edges of a convex polyhedron. Alternatively, in purely graph-theoretic terms, the polyhedral graphs are the 3-vertex-con ...
s with eight nodes).
In other fields
*The years
257 and
257 BC
*257 is the country calling code for
Burundi
Burundi (, ), officially the Republic of Burundi ( rn, Repuburika y’Uburundi ; Swahili language, Swahili: ''Jamuhuri ya Burundi''; French language, French: ''République du Burundi'' ), is a landlocked country in the Great Rift Valley at the ...
. See
List of country calling codes
Country calling codes or country dial-in codes are telephone number prefixes for reaching telephone subscribers in the networks of the member countries or regions of the International Telecommunication Union (ITU). The codes are defined by the ...
.
*
.257 Roberts
The .257 Roberts, also known as .257 Bob, is a medium-powered .25 caliber rifle cartridge. It has been described as the best compromise between the low recoil and flat trajectory of smaller calibers such as the 5 mm (.22") and 6 mm (.24"), and ...
, rifle cartridge
*There is a Pac-Man themed restaurant called
Level 257
Enterrium (formerly known as Level 257 then Pac-Man Entertainment) is a contemporary American restaurant and video arcade located at Woodfield Mall in Schaumburg, Illinois. The restaurant and entertainment destination was originally inspired by '' ...
located in
Schaumburg, Illinois
Schaumburg ( ) is a village mostly in Cook County and partly in DuPage County in northeastern Illinois, United States. Per the 2020 Census, the population was 78,723. Schaumburg is around northwest of the Chicago Loop and northwest of O'Hare I ...
. It is in reference to the
kill screen
''Kill Screen'' (stylized as ''KILL SCREEN'') was a print and online magazine founded in 2009 by Jamin Warren and Chris Dahlen and owned by Kill Screen Media, Inc. It focused on video games and culture, but also included articles based on ent ...
reached in Level 256 in the
Pac-Man
originally called ''Puck Man'' in Japan, is a 1980 maze action video game developed and released by Namco for arcades. In North America, the game was released by Midway Manufacturing as part of its licensing agreement with Namco America. Th ...
arcade game.
*
257ers is a German hip hop duo
References
{{DEFAULTSORT:257 (Number)
Integers