257 (two hundred [and] fifty-seven) is the natural number following 256 and preceding 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 | |||
| Senary | 11056 | |||
| Octal | 4018 | |||
| Duodecimal | 19512 | |||
| Hexadecimal | 10116 | |||
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]
Analogously, 257 is the third Sierpinski prime of the first kind, of the form ➜ .[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]
Four-fold 257 is 1028, which is the prime index of the fifth Mersenne prime, 8191.[7][8]
There are exactly 257 combinatorially distinct convex polyhedra with eight vertices (or polyhedral graphs with eight nodes).[9]
References
edit- ^ 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. Retrieved 2020-07-30.
- ^ Sloane, N. J. A. (ed.). "Sequence A006562 (Balanced primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000928 (Irregular primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002496 (Primes of form n^2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A014551 (Jacobsthal-Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000040 (The prime numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-02-21.
- ^ Sloane, N. J. A. (ed.). "Sequence A000668 (Mersenne primes (primes of the form 2^n - 1).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-02-21.
- ^ 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.