Re: twin primes and goldbach conjectures unprovable?

From: Craig Feinstein (cafeinst_at_msn.com)
Date: 08/05/04 

Date: 5 Aug 2004 07:37:08 -0700

David C. Ullrich <ullrich@math.okstate.edu> wrote in message news:<4044h01o1a9bnblbl2rdb3u74c2umbo0tm@4ax.com>...
> On 4 Aug 2004 15:10:21 -0700, cafeinst@msn.com (Craig Feinstein)
> wrote:
>
> >I made a few small corrections to make it clearer: Any comments are
> >welcome. I'm not claiming that it is a valid proof or not, but that it
> >is interesting.
>
> well you're wrong about that. the argument is utterly stupid,
> hence not interesting at all. [the fact that you keep posting
> this nonsense might interest some people, but not for mathematical
> reasons.]

Interesting is in the eyes of the beholder. In science, it is the
crazy ideas that make progress. One can choose to be a "conventional
mathematician" and publish boring stuff that no one reads, that
doesn't have any applications, become a tenured professor, criticize
others who have nonconventional ideas, gain some respect from your
peers, and then die, leaving absolutely no impact at all on science.

Or one can at least try to make some progress proposing crazy ideas,
not caring what people think or whether they accept them or not. Most
of these ideas will turn out to be ridiculous, but maybe one idea will
be correct. I chose this path. While traveling on this path, "the road
less traveled", one inevitably comes into contact with people stuck in
traffic on the main highway, who don't want to admit that they are the
fools that chose what appeared to be the more logical path, the main
highway, but in reality it was the wrong choice. They hate to admit
that people taking the backroads are beating them, getting to their
destination in less time.

>
> >---------------------
> >
> >The Twin Primes Conjecture states that there are infinitely many prime
> >numbers p such that p+2 is also prime. And Goldbach's Conjecture
> >states that every even number can be expressed as the sum of two prime
> >numbers. In this brief note, we show that the Twin Primes Conjecture
> >and Goldbach's Conjecture are impossible to prove true.
> >
> >Theorem 1: It is impossible to prove that the Twin Primes Conjecture
> >is true.
>
> my theorem: it is impossible to prove that there are infinitely
> many primes.
>
> >Proof: Let S be the set of all n such that 6n-1 is prime and let T be
> >the set of all n such that 6n+1 is prime. Then proving the Twin Primes
> >Conjecture is equivalent to showing that S intersect T is infinite.
>
> proof: let P be the set of primes.
>
> >Notice that if we did not know the values of an infinite number of
> >elements in
> >set S, we could not rule out the possibility S intersect T is finite,
> >since the condition that defines set S, that 6n-1 is prime if and only
> >if n is in S, does not rule out any possible factorizations of 6n+1
> >when n is in S. And notice that if we did not know the values of an
> >infinite number of elements in set T, we could not rule out the
> >possibility S
> >intersect T is finite, since the condition that defines set T, that
> >6n+1 is prime if and only if n is in T, does not rule out any possible
> >factorizations of 6n-1 when n is in T.
>
> note that since we do not know the value of infinitely many elements
> of P we cannot rule out the possibility that P is finite. qed.
>
> huh???????

You have given a completely different argument than my argument, so it
doesn't refute anything. Try to give an argument that at least
resembles my argument.

>
> your proof that the proof is impossible simply states that
> it's impossible, with no justification. why would anyone
> think that's interesting?

As I said, interesting is in the eyes of the beholder.

>
>
> ************************
>
> David C. Ullrich
>
> sorry about the inelegant formatting - typing
> one-handed for a few weeks...

Relevant Pages