quasi
Posts:
12,042
Registered:
7/15/05
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Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
Posted:
May 23, 2013 8:25 AM
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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
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