Re: [PrimeNumbers] Y AP (Yet Another Proof)
- In an email dated 19/6/2005 6:06:25 pm GMT Daylight time, Robin Garcia <sopadeajo2001@...> writes:
>I have not come across this assetion before.
>Is anybody interested in a proof that:
>For every natural number n, very is at least a prime of the form n^2+k^2 or (n^2+k^2)/2 for 1<=k<=n
For large n, it is very unlikely to be false, as there are n numbers of size O(n^2) being tested, and by PNT the probable no. of these that are prime is O(n/log(n^2)) which is >> 1.
>Jens,Mike,David,Chris, and others:I would be very interested in seeing your proof.
>Could you tell me if this has been already proven; and if not, if you consider it worth being published here?
>The proof is rather elemental,though long and tedious.