5657

5657 is a four-digit prime number in the decimal system. It is odd and greater than 2, with no positive divisors other than 1 and itself. A check of divisibility by primes up to the square root of 5657 (approximately 75) shows that no such prime divides 5657, confirming its primality.

In various numeral bases, 5657 appears as 1011000011001 in binary, 13031 in octal, and 1619 in hexadecimal. Its decimal digits are 5, 6, 5, and 7, which sum to 23; this sum indicates it is not divisible by 3 or 9.

Mathematically, a prime number congruent to 1 modulo 4 can be expressed as a sum of two squares. Accordingly, 5657 can be written as 61^2 + 44^2, since 61^2 equals 3721 and 44^2 equals 1936, summing to 5657.

Additional properties include its congruences: 5657 ≡ 1 (mod 4) and 5657 ≡ 2 (mod 3). Beyond these arithmetic characteristics, 5657 does not have a widely recognized special significance in science or culture; it is primarily noted in number theory as a prime in the four-digit range and for its representations in different bases.