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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: 12,012 Registered: 7/15/05
Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
Posted: May 23, 2013 8:25 AM

joshipura wrote:
>
>I am not a mathematician - but can understand prime numbers,
>and even the hypothesis under discussion.
>
>I wanted to tell to my children (who also know about prime
>
>"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 if p is a prime number, within
>p + 70,000,000 there is another prime number q, no matter
>how large p is.

No.

Let d = 70,000,000.

It's not true that for all primes p there is a prime q with
p < q <= p + d.

For example, let p be the largest prime less than (d + 1)! + 2
and let q be the least prime greater than p. Then q > p + d, so
there are no primes in the range p + 1 to p + d inclusive.

What was proved is that there are infinitely many primes pairs
p,q with p < q <= p + d.

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