5209

5209 is a natural number that follows 5208 and precedes 5210. In mathematics, it is a prime number.

It is odd and congruent to 1 modulo 4 (5209 ≡ 1 (mod 4)). As a prime of this form, 5209 can be expressed as a sum of two squares: 5209 = 72^2 + 5^2. Its primality also implies there are no nontrivial factors in the integers. In binary, 5209 is 1010001011001_2.

Beyond its basic numeric properties, 5209 is sometimes cited in recreational number theory as an example of a prime that can be written as a sum of two squares, illustrating the relationship between primes congruent to 1 modulo 4 and representations as sums of squares. The number also serves as a simple four-digit decimal example for discussions of base representations and primality, without carrying notable cultural or historical associations.