257 (number)

← 256 257 258 →
← 200 210 220 230 240 250 260 270 280 290 → List of numbers — Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	two hundred fifty-seven
Ordinal	257th (two hundred and fifty-seventh)
Factorization	257
Prime	yes
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 is the natural number between 256 and 258. It is also a prime number.

In mathematics

257 is a prime number of the form $2^{2^n}+1,$ 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

257 is the country calling code for Burundi. See List of country calling codes.

References

1. Hsiung, C. Y. (1995), Elementary Theory of Numbers, Allied Publishers, pp. 39–40, ISBN 9788170234647.
2. "Sloane's A006562 : Balanced primes", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
3. "Sloane's A000928 : Irregular primes", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
4. "Sloane's A002496 : Primes of form n^2 + 1", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
5. "Sloane's A014551 : Jacobsthal-Lucas numbers", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
6. "Sloane's A000944 : Number of polyhedra (or 3-connected simple planar graphs) with n nodes", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.