6829

6829 is a natural number that follows 6828 and precedes 6830. It is an odd prime, meaning its only positive divisors are 1 and 6829. Its digits sum to 25, so it is not divisible by 3, and it is congruent to 1 modulo 4.

In number theory, 6829 has the property that primes congruent to 1 mod 4 can be expressed as a sum of two squares. Indeed, 6829 = 77^2 + 30^2, illustrating this representation. The prime status also implies that this sum-of-squares decomposition is not unique in general for composite numbers, but for primes of this form it exists.

Other representations include its binary and hexadecimal forms. In binary, 6829 is 1101010101101₂, and in hexadecimal it is 0x1AAD. These representations can be useful in computing contexts where base conversions are relevant.

As a relatively small prime, 6829 does not have widely noted historical or scientific events associated with it, but it serves as an example of a prime that can be expressed as a sum of two squares and demonstrates common base-conversion forms.