4289

4289 is a natural number that follows 4288 and precedes 4290. It is odd and, more notably, a prime number, meaning it has no positive divisors other than 1 and itself. A check of divisors up to the square root (about 65) yields none, confirming primality.

In various numeral bases, 4289 has several representations: in binary it is 1000011000001, in hexadecimal 0x10C1, and in octal 10301. These representations reflect its size and factorization properties in different systems.

The sum of its decimal digits is 4 + 2 + 8 + 9 = 23, giving a digital root of 5. It is congruent to 1 modulo 4, and as a prime with this property, 4289 can be expressed as a sum of two squares: for example, 4289 = 65^2 + 8^2.

Beyond these arithmetic properties, 4289 does not have widely noted special significance in standard mathematical tables or widely cited constants. It is, however, a representative example of a prime that is not even, not divisible by small primes, and yet supports the two-squares representation theorem.