3457

3457 is a prime number in the decimal system. It is a four-digit natural number that lies between 3456 and 3458. In mathematics, 3457 is notable for its primality, meaning it has no positive divisors other than 1 and itself.

Properties of 3457 include that it is odd and not divisible by small primes such as 2, 3, or 5. A check of divisibility by primes up to the square root of 3457 (about 58.8) confirms its primality. It is congruent to 1 modulo 4, since 3457 ≡ 1 (mod 4). By Fermat's theorem on sums of two squares, every prime p ≡ 1 (mod 4) can be written as a sum of two squares; for 3457 one such representation is 3457 = 44^2 + 39^2.

In other bases, 3457 has concise representations: in binary it is 110110000001, and in hexadecimal it is 0xD81.

3457 appears primarily in mathematical contexts as an example of a four-digit prime with a straightforward sum-of-two-squares representation. It does not have wide-ranging cultural or historical associations beyond its role as a prime in number theory. See also prime number, sum of two squares, and Fermat’s theorem for related concepts.