## A good concise proof of the infinity of primes

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• http://www.mathreference.com/num,inf.html impressed me with this concise proof that there are Infinitely Many Primes Suppose there is a finite list of primes.
Message 1 of 2 , Dec 16, 2007
http://www.mathreference.com/num,inf.html

impressed me with this

concise proof that there are

Infinitely Many Primes

Suppose there is a finite list of primes.
Multiply them together and add 1, giving n.

Now n is not prime - it is larger than all the primes on our list,
which is suppose to be complete.

So n is composite.

Let p be a prime in the unique factorization of n.
Since p is on the list, it divides n-1, as well as n.
Hence it divides 1, which is impossible.

There are an infinite number of prime numbers.
• ... Good old Euclid has impressed many people. This is one of the most famous proofs in the history of mathematics. I have probably seen it over 100 times. I m
Message 2 of 2 , Dec 16, 2007
Kermit Rose:
> http://www.mathreference.com/num,inf.html
> impressed me with this concise proof that there are Infinitely Many Primes

Good old Euclid has impressed many people.
This is one of the most famous proofs in the history of mathematics.
I have probably seen it over 100 times.
I'm surprised if it's new to a frequent poster to this list.
If you want to pass 100 in a hurry then try