4877

4877 is a natural number that comes after 4876 and before 4878. In mathematics, 4877 is a prime number. It is not divisible by any integer other than 1 and itself, a fact that can be verified by checking divisibility by primes up to its square root. Because it is a prime congruent to 1 modulo 4, 4877 can be expressed as a sum of two squares; for example, 4877 = 61^2 + 34^2.

The representation of primes as sums of two squares is a classical topic in number theory, and primes of the form 4k+1 are known to admit such representations uniquely up to order and signs. The pair (61, 34) provides an explicit instance for 4877. In modular arithmetic and related areas, primes like 4877 often appear in discussions of quadratic forms, lattice points on circles, and algorithms for primality testing.

Outside pure mathematics, 4877 can serve as a numerical identifier in various contexts, such as cataloging, sequencing, or labeling in datasets. As with most integers, its properties are studied within broader mathematical frameworks rather than as an isolated fact.

See also: prime numbers, sum of two squares, Fermat’s theorem on sums of two squares.