523

523 is a natural number that comes after 522 and before 524. In mathematics, it is classified as an odd prime number, meaning its only positive divisors are 1 and itself. As such, 523 is part of the set of primes and is used in discussions of primality, factorization, and related number-theory topics.

In different numeral systems, 523 has several distinct representations. In binary it is 1000001011, in octal 1013, and in hexadecimal 0x20B. In Roman numerals it is written as DXXIII. The decimal digits sum to 10, and the number’s digital root is 1.

As a prime congruent to 3 modulo 4 (since 523 ≡ 3 mod 4), 523 cannot be expressed as a sum of two integer squares. This is a standard consequence of number-theoretic results about primes in forms congruent to 3 modulo 4. Its primality also implies it has no nontrivial factorization, which underpins many of its theoretical properties in arithmetic.

523 is often encountered as an example in introductory discussions of primes, base conversions, and modular arithmetic. While it does not carry widely known historical or cultural associations on its own, it serves as a representative case for exploring fundamental properties of prime numbers in the 500s.