257 (number)

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← 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
Hexadecimal10116
VigesimalCH20
Base 367536

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

In mathematics[edit]

257 is a prime number of the form 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]

In other fields[edit]

References[edit]

  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.