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Topic: First Proof That Infinitely Many Prime Numbers Come in Pairs
Replies: 30   Last Post: May 28, 2013 6:01 AM

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 quasi Posts: 12,067 Registered: 7/15/05
Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
Posted: May 24, 2013 2:03 AM

joshipura wrote:

>OK. So here goes changed script for review:
>
>"For years mathematicians are struggling to prove that they
>will always find larger and larger cases of p where p and p+2
>both are primes.
>
>Someone recently proved that
>**
>there are as many prime numbers p and q less than 70,000,000
>apart as you want
>**

Yes, In a sense.

The phrase "as many as you want" can be interpreted as
"infinitely many" (provided you always want more and more).

>So, now mathematicians will work on finding what types of
>p's this 70 million is negotiable to smaller numbers,
>eventually going down to 2."

It's not likely that they'll discover a classification for
the primes which have nearby successor primes.

They simply need to show, for a given integer d >= 2, that
there are infinitely prime pairs p,q with p < q <= p + d.

But yes, the goal is to keep reducing the value of d for which
they can prove the existence of infinitely many such prime pairs,
all the way down to d = 2, if possible.

quasi

Date Subject Author
5/16/13 Sam Wormley
5/16/13 Pubkeybreaker
5/16/13 Wally W.
5/17/13 Richard Tobin
5/17/13 Pubkeybreaker
5/17/13 Richard Tobin
5/17/13 Brian Q. Hutchings
5/18/13 Richard Tobin
5/18/13 Brian Q. Hutchings
5/18/13 Graham Cooper
5/19/13 Richard Tobin
5/23/13 Phil Carmody
5/25/13 Tucsondrew@me.com
5/17/13 David C. Ullrich
5/23/13 joshipura@gmail.com
5/23/13 quasi
5/24/13 joshipura@gmail.com
5/24/13 Graham Cooper
5/24/13 quasi
5/24/13 Graham Cooper
5/24/13 Pubkeybreaker
5/23/13 Peter Percival
5/23/13 Brian Q. Hutchings
5/23/13 Brian Q. Hutchings
5/24/13 Robin Chapman
5/24/13 Brian Q. Hutchings
5/24/13 Brian Q. Hutchings
5/28/13 Robin Chapman
5/24/13 Robin Chapman
5/25/13 byron
5/25/13 Brian Q. Hutchings