Re: The number of primes in the interval (0, m)
- --- In email@example.com,
> David. You are skeptical about my result.Dorogoi chitatel' / Dear reader
It's worse than that: you have no "result" for m > 40291.
For real m and positive integer n let
Q(m,n) = m*prod(k=1,n,1 - 1/prime(k)) + n - 1,
pi(m) = number of primes not exceeding m.
In http://tinyurl.com/2w73pef you conjectured that
Q(m,pi(sqrt(m))) = pi(m) ................... 
has an infinite number of solutions:
> The Number Theory "Number of primes in intervals"I claim that this is false, since
> "A million dollar problem"
> Friday, 2 April 2010
> Infinite number of figures (m_Q)
Q(m,pi(sqrt(m))) > pi(m), for m > 40291 .... 
You keep posting messages about "error in calculation".
But yours was an "error in understanding": the left
and right hand sides of  are clearly incommensurable,
at large m, for the very good reason that 2 > exp(Euler).
Little is served by comparing things that *always* differ,
for m > 40291.
Let's take an example, using http://primes.utm.edu/nthprime/
m = 29996224275833
pi(m) = 1000000000000
n = pi(sqrt(m)) = 379312
Q(m,n) = 1085398179034.020151103297662104429...
Q(m,n) - pi(m) > 85398179034
So here your "error in calculation" exceeds 85 billion.
Konets istorii? / End of story?