4261

4261 is the natural number that follows 4260 and precedes 4262. In mathematics, it is notable for being a prime number. It is odd and congruent to 1 modulo 4 (4261 ≡ 1 (mod 4)). As a prime of this congruence class, 4261 can be expressed as a sum of two squares: 4261 = 65^2 + 6^2. This representation is essentially unique up to order and sign, a consequence of Fermat’s theorem on sums of two squares.

In binary, 4261 is represented as 1000010100101.

Its decimal digits sum to 13, so it is not divisible by 3, and it does not end in 0 or 5, so it is not divisible by 2 or 5. A check for factors up to the square root (around 65) reveals no divisors other than 1 and itself, confirming primality.

Within number theory, 4261 is categorized among primes congruent to 1 modulo 4 and serves as a concrete example of the two-squares property. Beyond its mathematical properties, 4261 does not have widely recognized special meanings in standard historical, cultural, or scientific contexts and is typically encountered in discussions of prime numbers and elementary representations as sums of squares.