5113

5113 is a positive integer that, in the field of mathematics, is identified as a prime number. It has no positive divisors other than 1 and itself, and its primality can be verified by checking divisibility against primes up to its square root (approximately 71). The number is congruent to 1 modulo 4, a property shared by primes that can be expressed as the sum of two squares.

In line with Fermat’s two-square theorem, 5113 can be represented as a sum of two squares: 5113 = 48^2 + 53^2. This representation confirms its status as a prime of the form 4k + 1 and illustrates a classic property of such primes.

5113 also has straightforward representations in common numeral bases: in binary it is 1001111111001, in octal it is 11771, and in hexadecimal it is 0x13F9. These alternative bases can be useful in computer science and digital systems, where binary and hexadecimal forms are frequently used.

As a four-digit decimal prime, 5113 appears in various mathematical lists and algorithms as a representative example of primes in small ranges. Its factorization properties, base representations, and the sum-of-squares expression render it a concise illustration of several standard number-theory concepts.