Natural number
257 (two hundred [and] fifty-seven) is the natural number following256 and preceding258.
257 is aprime number of the form
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 form
➜
.[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]
- ^Hsiung, C. Y. (1995),Elementary Theory of Numbers, Allied Publishers, pp. 39–40,ISBN 9788170234647.
- ^Weisstein, Eric W."Sierpiński Number of the First Kind".mathworld.wolfram.com. Retrieved2020-07-30.
- ^Sloane, N. J. A. (ed.)."Sequence A006562 (Balanced primes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^Sloane, N. J. A. (ed.)."Sequence A000928 (Irregular primes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^Sloane, N. J. A. (ed.)."Sequence A002496 (Primes of form n^2 + 1)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^Sloane, N. J. A. (ed.)."Sequence A014551 (Jacobsthal-Lucas numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^Sloane, N. J. A. (ed.)."Sequence A000040 (The prime numbers.)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2024-02-21.
- ^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.
- ^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.
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400 to 999 |
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1000s and 10,000s |
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100,000s to 10,000,000,000,000s |
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- 100,000
- 1,000,000
- 10,000,000
- 100,000,000
- 1,000,000,000
- 10,000,000,000
- 100,000,000,000
- 1,000,000,000,000
- 10,000,000,000,000
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