> On 06/09/17 17:27, Isaac M. Bavaresco wrote:
> > Dear All,
> >
> >
> > Today I woke up with a silly idea about prime numbers in my head:
> >
> > What is the proof that there are infinitely many prime numbers? One of
> > such proofs was in my mind.
> >
> > Then I Googled and found Euclid's Proof. It is much similar to mine but
> > not exactly the same.
> >
> >
> > My proof:
> >
> > Consider a finite list of consecutive prime numbers starting in 3: 3, 5,
> > 7, 11, ..., Pn.
> >
> > Let P be the product of all the prime numbers in the list.
> >
> > Let Q = P + 2. Let's prove that Q is prime:
> >
> > P + 1 is even (not prime)
> >
> > P + 3 is multiple of 3 (not prime)
> >
> > P + 5 is multiple of 5 (not prime)
> >
> > ...
> >
> > P + Pn is multiple of Pn (not prime)
> >
> >
> > So Q cannot be multiple of any of the numbers in the list,
> True
> > thus Q is prime.
> This is where you go wrong.
>
> There may be prime numbers which are larger than Pn but smaller than Q.
> Some of these could conceivably be factors of Q.
>
> For example
>
> (3x5x7x11)+2 = 1157 = 13*89
>
> So while this proves there is at least one prime that is not on your list
> (and hence proves there are infinitely many primes) it does not provide an
> efficient method for actually finding large primes.
> --
>
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