6553

6553 is a positive integer that follows 6552 and precedes 6554. In mathematics, it is a prime number, meaning its only positive divisors are 1 and itself. As a result, it has no nontrivial factorization.

In base representations, 6553 appears as 0x1999 in hexadecimal, 14631 in octal, and 1100110011001 in binary. These representations illustrate a repeating pattern in binary and a compact hex form that is sometimes noted in discussions of numeral bases. The decimal digits of 6553 sum to 19, so the number is congruent to 1 modulo 9, and it is also congruent to 1 modulo 8 and modulo 3.

Because 6553 is prime, its factorization consists only of 1 and 6553. It is not a Sophie Germain prime, since 2 × 6553 + 1 equals 13107, which factors as 3 × 17 × 257. Thus, while 6553 is prime, it does not have the additional property required to be classified as Sophie Germain.

See also: list of prime numbers, hexadecimal notation, binary numeral system.