# 257 (number)

 ← 256 257 258 →
Cardinal two hundred and 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
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 $2^{2^3}+1$ 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. It is also a Proth prime. And since it is of the form 4n + 1, it is a Pythagorean prime.

It is also an irregular prime, and a long prime (in base 10) and a balanced prime. Since the next prime, 263, is 6 away, 257 is called a sexy prime.

Since 257 + 2 = 259, a semiprime, 257 is a Chen prime. It is also an Eisenstein prime with no imaginary part, and a Pierpont prime.

257 is the hypotenuse of a primitive Pythagorean triple: $257^{2} = 32^{2}+255^{2}$

## In other fields

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