4789

4789 is a natural number that follows 4788 and precedes 4790. It is an odd integer and, in number theory, is notable for being a prime number, meaning its only positive divisors are 1 and itself.

As a prime, 4789 has no smaller divisors. A primality check up to the square root of 4789 (approximately 69) confirms that no prime number less than or equal to 69 divides it. Consequently, its divisor set is {1, 4789}.

In modular arithmetic, 4789 satisfies several simple congruences: for example, 4789 ≡ 1 (mod 3) and 4789 ≡ 1 (mod 4). These traits follow from the sum of digits and the last two digits of the number, respectively.

4789 has standard representations in several numeral systems. In binary, it is 1001010110101. In octal, it is 11265. In hexadecimal, it is 12B5. In classical Roman numerals, it can be written as MMMMDCCLXXXIX, representing 4000 (MMMM) plus 700 (DCC) plus 80 (LXXX) plus 9 (IX).

Because of its prime status and its base representations, 4789 is sometimes referenced in discussions of prime testing, numeral systems, and the relationships between different bases. As with other primes, its properties make it a simple yet useful example in introductory number theory.