4657 has 2 divisors, whose sum is σ = 4658. Its totient is φ = 4656.

The previous prime is 4651. The next prime is 4663. The reversal of 4657 is 7564.

It is a balanced prime because it is at equal distance from previous prime (4651) and next prime (4663).

It can be written as a sum of positive squares in only one way, i.e., 3136 + 1521 = 56^2 + 39^2 .

It is a cyclic number.

It is not a de Polignac number, because 4657 - 2³ = 4649 is a prime.

It is a Chen prime.

It is a pancake number, because a pancake can be divided into 4657 parts by 96 straight cuts.

It is a nialpdrome in base 6.

It is not a weakly prime, because it can be changed into another prime (4651) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 2328 + 2329.

It is an arithmetic number, because the mean of its divisors is an integer number (2329).

2⁴⁶⁵⁷ is an apocalyptic number.

It is an amenable number.

4657 is a deficient number, since it is larger than the sum of its proper divisors (1).

4657 is an equidigital number, since it uses as much as digits as its factorization.

4657 is an odious number, because the sum of its binary digits is odd.

The product of its digits is 840, while the sum is 22.

The square root of 4657 is about 68.2422156733. The cubic root of 4657 is about 16.6994465974.

Adding to 4657 its reverse (7564), we get a palindrome (12221).

It can be divided in two parts, 4 and 657, that multiplied together give a triangular number (2628 = T₇₂).

The spelling of 4657 in words is "four thousand, six hundred fifty-seven".