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"new prime" argument was confusing
The smallest prime numbers are 2, 3, 5, 7, 11, 13... . An exmple of a composite number is 6, which is evenly divisible by both 2 and 3.
The smallest prime numbers are 2, 3, 5, 7, 11, 13... . An exmple of a composite number is 6, which is evenly divisible by both 2 and 3.
It is easy to prove that there are an infinite number of primes. If there were a finite number of primes, you could multiply them all together and add 1. The resulting number would have to be a new prime, since it would not be divisible by any smaller prime (it would always have a remainder of 1).
It is easy to prove that there are an infinite number of primes. If there were a finite number of primes, you could multiply them all together and add 1. The resulting number would show the existence of a new prime, since it would not be divisible by any smaller prime (it would always have a remainder of 1).