<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> 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>
why is 1 not the smallest prime number
why is 1 not the smallest prime number
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
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