A good concise proof of the infinity of primes
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.
- Kermit Rose:
> http://www.mathreference.com/num,inf.htmlGood old Euclid has impressed many people.
> impressed me with this concise proof that there are Infinitely Many Primes
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
Jens Kruse Andersen