257 (number)

Short description: Natural number
 ← 256 257 258 →
Cardinaltwo hundred fifty-seven
Ordinal257th
(two hundred fifty-seventh)
Factorizationprime
Primeyes
Greek numeralΣΝΖ´
Roman numeralCCLVII
Binary1000000012
Ternary1001123
Quaternary100014
Quinary20125
Senary11056
Octal4018
Duodecimal19512
VigesimalCH20
Base 367536

257 (two hundred [and] fifty-seven) is the natural number following 256 and preceding 258.

257 is a prime number of the form $\displaystyle{ 2^{2^n}+1, }$ specifically with n = 3, and therefore a Fermat prime. Thus a regular polygon with 257 sides is constructible with compass and unmarked straightedge. It is currently the second largest known Fermat prime.[1]

Analogously, 257 is the third Sierpinski prime of the first kind, of the form $\displaystyle{ n^{n} + 1 }$$\displaystyle{ 4^{4} + 1 = 257 }$.[2]

It is also a balanced prime,[3] an irregular prime,[4] a prime that is one more than a square,[5] and a Jacobsthal–Lucas number.[6]

There are exactly 257 combinatorially distinct convex polyhedra with eight vertices (or polyhedral graphs with eight nodes).[7]