4493

4493 is a positive integer that follows 4492 and precedes 4494. In the field of mathematics, 4493 is a prime number, meaning it has no positive divisors other than 1 and itself. Its primality can be established by trial division: testing possible factors up to its square root (approximately 67) yields no divisors, so 4493 is considered prime.

In various numeral systems, 4493 has the representations: decimal 4493; binary 1000110001101; octal 10615; and hexadecimal 0x118D. In Roman numerals it can be written as MMMMCDXCIII, though some conventions prefer alternative notations such as using overlines for large values.

Some basic modular properties of 4493 include that it is odd and congruent to 1 modulo 4 (4493 ≡ 1 mod 4). The sum of its digits is 20, so it is not divisible by 3. It is not divisible by 2, 5, or any other small prime beyond those checked through its square root.

There is no widely recognized historical or cultural significance attached to the number 4493, and it does not correspond to a well-known constant, year, or designation in common reference works. As a prime, it may appear in theoretical contexts within number theory and combinatorics, particularly in discussions of prime distribution and modular arithmetic.