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Re: prove no largest prime
Posted:
Jul 4, 2012 4:55 PM
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"Tim923" <tim.news@hotmail.com> wrote in
news:jt295f$217$1@dont-email.me:
> I've seen the simple proof of no largest prime a few times.
Something
> like:
>
> assume x is largest prime: 2,3,5,7,11....,x
> x+1,x+2,x+3 all composite
> add 1 to x to show no largest prime
>
> Is there a long proof that doesn't use contradiction?
You can show that the sum of the reciprocals of the
primes diverges, and conclude that there are infinitely
many primes.
http://en.wikipedia.org/wiki/Divergence_of_the_sum_of_the_reciprocal
s_of_the_primes
B.
--
Cheerfully resisting change since 1959.
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