piclist 2017\09\06\192810a >
Thread: Prime numbers
face picon face BY : Sean Breheny email (remove spam text)

Peter has a good point - if you also show that all integers have prime
factorizations (easy to do) then your method DOES prove that there are
infinitely many primes because it proves that there exists an integer Q,
larger than Pn, which is not divisible by any of the primes below (or equal
to) Pn - so either this number Q is itself prime, in which case you've
found a prime which is not in your original set, or if Q is not prime, it
must be divisible by at least one prime factor which is not contained in
your original set. Since Q is not even, this prime factor is not 2. Since
your set contains all primes between 2 and Pn, inclusive of Pn, you have
shown that there is at least one prime which is not in your set but is
larger than Pn.

On Wed, Sep 6, 2017 at 3:56 PM, peter green <spam_OUTplugwashKILLspamspamp10link.net> wrote:

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Subject (change) Prime numbers

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