

A Ridiculously Advanced Proof of a Simple Theorem - DaniFong
http://weblog.fortnow.com/2008/08/ridiculously-hard-proof-of-easy-theorem.html

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henning
Let's see if I still remember second year math.

Suppose the number of primes is finite, call them p1, p2, ..., pn. Let P be
their product, P = p1 _..._ pn. Since P > pi for all i, P+1 is not prime.
Therefore some pk divides P+1. but pk also divides P since it is in the list
of primes multiplied. Sp pk|((P+1)-P), i.e. pk|1, a contradiction. Therefore
the number of primes is infinite.

That proof depends on the fundamental theorem of arithmetic, and a theorem
that says that if p|X and p|Y then p|(X-Y).

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sysop073
I'm not sure where "Since P > pi for all i, P+1 is not prime" comes from, but
maybe I'm just misunderstanding you. I think you're trying to state this
proof:
[http://en.wikipedia.org/wiki/Prime_number#There_are_infinite...](http://en.wikipedia.org/wiki/Prime_number#There_are_infinitely_many_prime_numbers)

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sh1mmer
I was interested in the comment on the blog post, that you should be able to
validate any proofs you use or at least have a good excuse.

I think this is a general good practice for life. Extolling the work of others
that you don't understand, will not often end well. Particularly if someone
questions you about that work and it's implications.

