6673

6673 is a natural number that comes after 6672 and before 6674. It is a prime number, meaning its only positive divisors are 1 and itself. A check of divisibility by primes up to the square root of 6673 (which is about 81) shows that it is not divisible by any of 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, or 79, confirming its primality.

Due to the fact that 6673 ≡ 1 (mod 4), it can be expressed as a sum of two squares. A concrete representation is 63^2 + 52^2 = 3969 + 2704 = 6673, illustrating this property.

In common numeral systems, 6673 has the following representations: in binary it is 1101000010001, in octal it is 15021, and in hexadecimal it is 1A11. These representations reflect the same value across different bases.

From a mathematical standpoint, 6673 is an odd prime with a nontrivial representation as a sum of two squares. It sits within the broader study of prime numbers and their properties, including representations as sums of squares and their behavior under various modular conditions. There are no widely noted historical or cultural usages of 6673 as a specific designation beyond its role as a natural number in mathematical contexts.