4723

4723 is a natural number that follows 4722 and precedes 4724. In mathematics, it is an odd prime number, meaning its only positive divisors are 1 and 4723. Its primality can be verified by testing divisibility by primes up to its square root (approximately 68.7); none of the primes up to 67 divide 4723.

As a prime, 4723 cannot be expressed as a sum of two squares since it is congruent to 3 modulo 4. It is not a Sophie Germain prime, since 2·4723 + 1 equals 9447, which is divisible by 3 and thus not prime.

Numeral representations for 4723 include: in binary, 1001001110011; in hexadecimal, 0x1273; in octal, 11163_8. In Roman numerals, 4723 can be written as MMMMDCCXXIII in traditional forms that use four thousands without an overline; modern conventions often place a bar over the thousands to indicate 4,000, but alternative notations such as MMMMDCCXXIII are also encountered.

Beyond pure mathematics, 4723 may appear as an identifier or catalog number in various contexts (such as product codes or article numbering), but this article treats 4723 strictly as a numeric value and highlights its basic properties and representations.