On Thursday, May 23, 2013 5:48:03 PM UTC+5:30, quasi wrote: > 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
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 **
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."