Composite number

A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Accordingly, it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, or the unit 1, so the composite numbers are exactly the natural numbers that are not prime and not a unit. For example, the integer 14 is a composite number because it is the product of the two smaller integers 2 and 7; however, the integers 2 and 3 are not because each can only be divided by one and itself. The first 25 composite numbers (all up to 36) are: Every composite number can be written as the product of two or more (not necessarily distinct) primes. For example, the composite number 299 can be written as 13 × 23, and the composite number 360 can be written as 23 × 32 × 5; furthermore, this representation is unique up to the order of the factors. This fact is called the fundamental theorem of arithmetic. There are several known primality tests that can determine whether a number is prime or composite, which do not necessarily reveal the factorization of a composite input. Grimm's conjecture states that, for every set of consecutive composite numbers, there is an equally sized set of prime numbers, and a bijection mapping each composite in the former set to a prime in the latter set that it is divisible by.