<P> A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself . A natural number greater than 1 that is not a prime number is called a composite number . For example, 5 is prime because 1 and 5 are its only positive integer factors, whereas 6 is composite because it has the divisors 2 and 3 in addition to 1 and 6 . The fundamental theorem of arithmetic establishes the central role of primes in number theory: any integer greater than 1 is either a prime itself or can be expressed as a product of primes that is unique up to ordering . The uniqueness in this theorem requires excluding 1 as a prime because one can include arbitrarily many instances of 1 in any factorization, e.g., 3, 1 3, 1 1 3, etc. are all valid factorizations of 3 . </P> <P> The property of being prime is called primality . A simple but slow method of verifying the primality of a given number n is known as trial division . It consists of testing whether n is a multiple of any integer between 2 and n (\ displaystyle (\ sqrt (n))). Algorithms much more efficient than trial division have been devised to test the primality of large numbers . These include the Miller--Rabin primality test, which is fast but has a small probability of error, and the AKS primality test, which always produces the correct answer in polynomial time but is too slow to be practical . Particularly fast methods are available for numbers of special forms, such as Mersenne numbers . As of January 2016, the largest known prime number has 22,338,618 decimal digits . </P>

Why is 1 not the smallest prime number