email@example.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