<Dl> <Dd> N = p 1 ′ ⋅ p 2 ′ ⋯ p m ′ (\ displaystyle N = p'_ (1) \ cdot p'_ (2) \ cdots p'_ (m)) </Dd> </Dl> <Dd> N = p 1 ′ ⋅ p 2 ′ ⋯ p m ′ (\ displaystyle N = p'_ (1) \ cdot p'_ (2) \ cdots p'_ (m)) </Dd> <P> with one or more prime factors . N (\ displaystyle N) is evenly divisible by each of these factors, but N (\ displaystyle N) has a remainder of one when divided by any of the prime numbers in the given list, so none of the prime factors of N (\ displaystyle N) can be in the given list . Because there is no finite list of all the primes, there must be infinitely many primes . </P> <P> The numbers formed by adding one to the products of the smallest primes are called Euclid numbers . The first five of them are prime, but the sixth, </P>

When is a number called a factor of a number