Movatterモバイル変換

[0]ホーム
URL:

Jump to content
WikipediaThe Free Encyclopedia
Search

257 (number)

From Wikipedia, the free encyclopedia
Natural number
← 256257 258 →
Cardinaltwo hundred fifty-seven
Ordinal257th
(two hundred fifty-seventh)
Factorizationprime
Primeyes
Greek numeralΣΝΖ´
Roman numeralCCLVII,cclvii
Binary1000000012
Ternary1001123
Senary11056
Octal4018
Duodecimal19512
Hexadecimal10116

257 (two hundred [and] fifty-seven) is the natural number following256 and preceding258.

257 is aprime number of the form22n+1,{\displaystyle 2^{2^{n}}+1,} specifically withn = 3, and therefore aFermat prime. Thus, aregularpolygon with 257 sides isconstructible with compass and unmarked straightedge. It is currently the second largest known Fermat prime.[1]

Analogously, 257 is the thirdSierpinski prime of the first kind, of the formnn+1{\displaystyle n^{n}+1} ➜44+1=257{\displaystyle 4^{4}+1=257}.[2]

It is alsoabalanced prime,[3]anirregular prime,[4]a prime that is one more than a square,[5]and aJacobsthal–Lucas number.[6]

Four-fold 257 is1028, which is the prime index of the fifthMersenne prime,8191.[7][8]

There are exactly 257 combinatorially distinctconvex polyhedra with eightvertices (orpolyhedral graphs with eight nodes).[9]

References

[edit]
  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. Retrieved2020-07-30.
  3. ^Sloane, N. J. A. (ed.)."Sequence A006562 (Balanced primes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^Sloane, N. J. A. (ed.)."Sequence A000928 (Irregular primes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^Sloane, N. J. A. (ed.)."Sequence A002496 (Primes of form n^2 + 1)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. ^Sloane, N. J. A. (ed.)."Sequence A014551 (Jacobsthal-Lucas numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. ^Sloane, N. J. A. (ed.)."Sequence A000040 (The prime numbers.)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2024-02-21.
  8. ^Sloane, N. J. A. (ed.)."Sequence A000668 (Mersenne primes (primes of the form 2^n - 1).)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2024-02-21.
  9. ^Sloane, N. J. A. (ed.)."Sequence A000944 (Number of polyhedra (or 3-connected simple planar graphs) with n nodes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  •  0 
  •  1 
  •  2 
  •  3 
  •  4 
  •  5 
  •  6 
  •  7 
  •  8 
  •  9 


Stub icon

This article about anumber is astub. You can help Wikipedia byexpanding it.

Retrieved from "https://en.wikipedia.org/w/index.php?title=257_(number)&oldid=1265585500"
Categories:
Hidden categories:
[8]ページ先頭
©2009-2025 Movatter.jp