257 (number)
| ||||
|---|---|---|---|---|
| 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 | |||
| Hexadecimal | 10116 | |||
| Vigesimal | CH20 | |||
| Base 36 | 7536 | |||
257 (two hundred [and] fifty-seven) is the natural number following 256 and preceding 258.
257 is a prime number of the form [math]\displaystyle{ 2^{2^n}+1, }[/math] 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 [math]\displaystyle{ n^{n} + 1 }[/math] ➜ [math]\displaystyle{ 4^{4} + 1 = 257 }[/math].[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
- ↑ Hsiung, C. Y. (1995), Elementary Theory of Numbers, Allied Publishers, pp. 39–40, ISBN 9788170234647, https://books.google.com/books?id=Bfvbx85FkVQC&pg=PA39.
- ↑ Weisstein, Eric W.. "Sierpiński Number of the First Kind" (in en). https://mathworld.wolfram.com/SierpinskiNumberoftheFirstKind.html.
- ↑ Sloane, N. J. A., ed. "Sequence A006562 (Balanced primes)". OEIS Foundation. https://oeis.org/A006562.
- ↑ Sloane, N. J. A., ed. "Sequence A000928 (Irregular primes)". OEIS Foundation. https://oeis.org/A000928.
- ↑ Sloane, N. J. A., ed. "Sequence A002496 (Primes of form n^2 + 1)". OEIS Foundation. https://oeis.org/A002496.
- ↑ Sloane, N. J. A., ed. "Sequence A014551 (Jacobsthal-Lucas numbers)". OEIS Foundation. https://oeis.org/A014551.
- ↑ Sloane, N. J. A., ed. "Sequence A000944 (Number of polyhedra (or 3-connected simple planar graphs) with n nodes)". OEIS Foundation. https://oeis.org/A000944.
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