Re: sketch of small step in big proof
- From: Gerry Myerson <gerry@xxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Tue, 14 Oct 2008 01:57:08 GMT
In article
<11919668.1223914368039.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
daniel t <daniel6874@xxxxxxxxx> wrote:
The probability of finding a prime number is about 1/log(n).
This is a very loose way of speaking. Interpreted carefully,
it can guide you to true statements. Interpreted carelessly,
it leads to nonsense.
Look at the subinterval, 10^12 + 10000, 10^12 + 20000. This contains 10,000
numbers and we expect to find (1/(12log(10))*10000 primes--or 362 primes. In
fact there are 389.
So now my hopefully better question. I think that primes are *on this scale*
classically uniform.
Everybody thinks that primes are, on this scale, uniform
(modulo making that word, uniform, precise). Nobody has
a clue as to how to prove it, and everybody, with perhaps
one exception, knows that its negation is consistent with
the Prime Number Theorem.
--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.
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