8609

8609 is a natural number that follows 8608 and precedes 8610. It is an odd integer and is prime in the set of positive integers, having no positive divisors other than 1 and itself. Its primality can be verified by checking divisibility with primes up to its square root.

In number theory, 8609 has a couple of notable properties. It satisfies 8609 ≡ 1 (mod 4), which implies it can be expressed as a sum of two squares. Indeed, 8609 = 80^2 + 47^2. As a consequence, in the Gaussian integers, 8609 factors as (80 + 47i)(80 − 47i), reflecting its representation as a product of conjugate Gaussian integers.

Other simple representations include its binary form, which is 10000110100001. The representation as a sum of two squares confirms its status as a prime of the form p ≡ 1 (mod 4) and highlights a basic connection to two-square representations in modular arithmetic and complex integer factorization.