--- On Mon, 8/15/11, Roahn Wynar <

rwynar@...> wrote:

> I am looking for two proofs and don't know where to start.

>

> First, I seek the proof that the Gamma function is not the

> solution of any ordinary differential equation with rational

> coeficients. I have seen this proof refered to but

> have never actually seen it. Is it somehow obvious?

>

> Also, I am looking for an interesting proof that depends on

> the Reimann

Riemann. Try to forget the pronunciation of it that you learnt too, as it's almost certainly wrong (and leads to the misspelling). Once you have the correct pronunciation in your head, the correct spelling should follow automatically.

> Hypothesis being assumed true. The larger the

> implications of what ever proof you suggest the

> better. I would like to use it as an example in a

> short piece I am writing.

Maximum gaps between prime numbers

http://primes.utm.edu/notes/gaps.html ?

Maximum number of tests required for Miller-Rabin to prove primality?

I'm not sure there are any "implications", though. As not one single bit will be different in any algorithmic computation no matter if RH is true or false[*]. In the real world, we're usually happy to just say "the probability of X is <= 10^-big, or >= 1-10^-big".

You have to remember that the real world is where supposed numerate people (economists) are prepared to pretend the cauchy distribution has a mean and a standard deviation. 91 might as well be prime, and the Riemann Hypothesis might as well be a piece of blank verse, in the face of such ignorance.

Phil

[* Not strictly true, as RH can tell you to stop earlier, for example, but that basically only changes the bailing out conditions (failures to find something), not the actual numbers you'd rather be finding.]