4637

4637 is a natural number that follows 4636 and precedes 4638. In mathematics, 4637 is a prime number, meaning it has exactly two distinct positive divisors: 1 and itself. It is odd and congruent to 1 modulo 4, a property that aligns with primes of the form 4k+1.

Because primes p ≡ 1 mod 4 can be expressed as a sum of two squares, 4637 can be written as 4637 = 59^2 + 34^2. In common bases, 4637 is represented as 1001000011101 in binary and as 0x121D in hexadecimal.

Aside from its status as a four-digit prime, 4637 does not have a widely noted mathematical significance beyond being used as an example in discussions of primality, modular arithmetic, and number representations. It is included in the natural-number sequence of integers and can appear in various cataloging or coding contexts where small prime numbers are used.

See also: 4636, 4638.