Date: May 23, 2013 8:47 AM
Author: Peter Percival
Subject: Re: First Proof That Infinitely Many Prime Numbers Come in Pairs

joshipura@gmail.com 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.


There is a theorem that there is no upper limit on the number of
consecutive composites. Suppose you want at least n-1, (n >= 2)
consecutive composites, consider

n! + 2, n! + 3, n! + 4, ..., n! + n.

> 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."
>
> Is my understanding correct?
>



--
I think I am an Elephant,
Behind another Elephant
Behind /another/ Elephant who isn't really there....
A .A. Milne