7927

7927 is a natural number that follows 7926 and precedes 7928. In mathematics, it is notable for being a prime number. Its primality is established by the absence of divisors among the prime numbers up to its square root (approximately 89), as 7927 is not divisible by any prime less than or equal to 89.

In base representations, 7927 has several common forms. In binary it is 1111011110111_2. In octal it corresponds to 17367_8, and in hexadecimal it is 1EF7_16. These representations reflect its decimal value while highlighting the different numeral systems often used in computational contexts.

A property of 7927 arising from modular arithmetic is that it is congruent to 3 modulo 4 (7927 ≡ 3 (mod 4)). As a prime with this congruence, it cannot be expressed as a sum of two integer squares, a consequence of a classical result in number theory.

Beyond its basic status as a prime, 7927 does not have widely noted special significance in standard mathematical sequences or famous theorems. It commonly appears as an example value in discussions of primality, base conversion, and modular arithmetic. Its simplicity as a prime also makes it convenient in discussions about properties that apply to primes with certain modular constraints.