5197

5197 is a natural number that comes after 5196 and before 5198. It is a prime number, having no positive divisors other than 1 and itself.

The number is congruent to 1 modulo 4, since 5197 ≡ 1 (mod 4). By the two-squares theorem, a prime of the form 4k+1 can be expressed as a sum of two squares; for 5197 one such representation is 5197 = 66^2 + 29^2.

In base representations, 5197 is written as follows: in decimal it is 5197; in binary it is 1010001001101; in hexadecimal it is 0x144D; and in octal it is 12115.

Other straightforward properties include a digits sum of 22, giving a digital root of 4. The number is odd and, as noted, prime, which places it among the primes of the form 4k+1 that can be expressed as a sum of two squares.

As a mathematical object, 5197 serves as an example of a four-digit prime with a simple sum-of-squares representation. It does not have widely cited constants, events, or cultural associations beyond its role in number theory.