← 256 257 258 →
Cardinaltwo hundred fifty-seven
Ordinal257th
(two hundred fifty-seventh)
Factorizationprime
Primeyes
Greek numeralΣΝΖ´
Roman numeralCCLVII
Binary1000000012
Ternary1001123
Senary11056
Octal4018
Duodecimal19512
Hexadecimal10116

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]

## References

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. ^