← 256 257 258 →
Cardinaltwo hundred fifty-seven
Ordinal257th
(two hundred fifty-seventh)
Factorizationprime
Primeyes
Greek numeralΣΝΖ´
Roman numeralCCLVII
Binary1000000012
Ternary1001123
Senary11056
Octal4018
Duodecimal19512

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

257 is a prime number of the form $2^{2^{n))+1,$ 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.

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

It is also a balanced prime, an irregular prime, a prime that is one more than a square, and a Jacobsthal–Lucas number.

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

1. ^ Hsiung, C. Y. (1995), Elementary Theory of Numbers, Allied Publishers, pp. 39–40, ISBN 9788170234647.
2. ^ Weisstein, Eric W. "Sierpiński Number of the First Kind". mathworld.wolfram.com. Retrieved 2020-07-30.
3. ^ Sloane, N. J. A. (ed.). "Sequence A006562 (Balanced primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
4. ^ Sloane, N. J. A. (ed.). "Sequence A000928 (Irregular primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
5. ^ Sloane, N. J. A. (ed.). "Sequence A002496 (Primes of form n^2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
6. ^ Sloane, N. J. A. (ed.). "Sequence A014551 (Jacobsthal-Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
7. ^