• 257 can be written using four 4's:

257 has 2 divisors, whose sum is σ = 258. Its totient is φ = 256.

The previous prime is 251. The next prime is 263. The reversal of 257 is 752.

257 is nontrivially palindromic in base 2, base 4, base 7 and base 16.

It is a Cunningham number, because it is equal to 2^{8}+1.

257 is an esthetic number in base 16, because in such base its adjacent digits differ by 1.

It is a balanced prime because it is at equal distance from previous prime (251) and next prime (263).

It can be written as a sum of positive squares in only one way, i.e., 256 + 1 = 16^2 + 1^2 .

It is a cyclic number.

It is not a de Polignac number, because 257 - 2^{4} = 241 is a prime.

It is a Chen prime.

257 is an undulating number in base 7 and base 16.

It is a plaindrome in base 10, base 13, base 14 and base 15.

It is a congruent number.

It is a panconsummate number.

It is not a weakly prime, because it can be changed into another prime (251) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (2) of ones.

It is a good prime.

It is a Pierpont prime, being equal to 2^{8} ⋅ 3^{0} + 1.

In principle, a polygon with 257 sides can be constructed with ruler and compass.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 128 + 129.

It is an arithmetic number, because the mean of its divisors is an integer number (129).

It is a Proth number, since it is equal to 1 ⋅ 2^{8} + 1 and 1 < 2^{8}.

It is an amenable number.

257 is a deficient number, since it is larger than the sum of its proper divisors (1).

257 is an equidigital number, since it uses as much as digits as its factorization.

257 is an evil number, because the sum of its binary digits is even.

The product of its digits is 70, while the sum is 14.

The square root of 257 is about 16.0312195419. The cubic root of 257 is about 6.3578611797.

Subtracting from 257 its sum of digits (14), we obtain a 5-th power (243 = 3^{5}).

It can be divided in two parts, 25 and 7, that added together give a 5-th power (32 = 2^{5}).

The spelling of 257 in words is "two hundred fifty-seven", and thus it is an aban number.

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