257 (number)

 ← 256 257 258 →
Cardinal two hundred fifty-seven
Ordinal 257th
(two hundred fifty-seventh)
Factorization prime
Prime yes
Greek numeral ΣΝΖ´
Roman numeral CCLVII
Binary 1000000012
Ternary 1001123
Quaternary 100014
Quinary 20125
Senary 11056
Octal 4018
Duodecimal 19512
Vigesimal CH20
Base 36 7536

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

In mathematics

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]

It is also a balanced prime,[2] an irregular prime,[3] a prime that is one more than a square,[4] and a Jacobsthal–Lucas number.[5]

There are exactly 257 combinatorially distinct convex polyhedra with eight vertices (or polyhedral graphs with eight nodes).[6]

References

1. ^ Hsiung, C. Y. (1995), Elementary Theory of Numbers, Allied Publishers, pp. 39–40, ISBN 9788170234647.
2. ^ Sloane, N. J. A. (ed.). "Sequence A006562 (Balanced primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
3. ^ Sloane, N. J. A. (ed.). "Sequence A000928 (Irregular primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
4. ^ Sloane, N. J. A. (ed.). "Sequence A002496 (Primes of form n^2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
5. ^ Sloane, N. J. A. (ed.). "Sequence A014551 (Jacobsthal-Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
6. ^ Sloane, N. J. A. (ed.). "Sequence A000944 (Number of polyhedra (or 3-connected simple planar graphs) with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.