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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: 10,305
Registered: 7/15/05
Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
Posted: May 23, 2013 8:25 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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
>numbers) about this development. Here is my script:
>
>"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
Read First Proof That Infinitely Many Prime Numbers Come in Pairs
Sam Wormley
5/16/13
Read Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
Pubkeybreaker
5/16/13
Read Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
Wally W.
5/17/13
Read Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
Richard Tobin
5/17/13
Read Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
Pubkeybreaker
5/17/13
Read Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
Richard Tobin
5/17/13
Read Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
Brian Q. Hutchings
5/18/13
Read Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
Richard Tobin
5/18/13
Read Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
Brian Q. Hutchings
5/18/13
Read Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
Graham Cooper
5/19/13
Read Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
Richard Tobin
5/23/13
Read Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
Phil Carmody
5/25/13
Read Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
Tucsondrew@me.com
5/17/13
Read Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
David C. Ullrich
5/23/13
Read Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
joshipura@gmail.com
5/23/13
Read Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
quasi
5/24/13
Read Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
joshipura@gmail.com
5/24/13
Read Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
Graham Cooper
5/24/13
Read Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
quasi
5/24/13
Read Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
Graham Cooper
5/24/13
Read Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
Pubkeybreaker
5/23/13
Read Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
Peter Percival
5/23/13
Read Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
Brian Q. Hutchings
5/23/13
Read even numbers not the sum of TPs?
Brian Q. Hutchings
5/24/13
Read Re: even numbers not the sum of TPs?
Robin Chapman
5/24/13
Read Re: even numbers not the sum of TPs?
Brian Q. Hutchings
5/24/13
Read Re: even numbers not the sum of TPs?
Brian Q. Hutchings
5/28/13
Read Re: even numbers not the sum of TPs?
Robin Chapman
5/24/13
Read Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
Robin Chapman
5/25/13
Read Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
byron
5/25/13
Read Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
Brian Q. Hutchings

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