--- In

primenumbers@yahoogroups.com,

<chitatel2000@...> wrote:

> 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) ................... [1]

has an infinite number of solutions:

> The Number Theory "Number of primes in intervals"

> "A million dollar problem"

> Friday, 2 April 2010

> Infinite number of figures (m_Q)

I claim that this is false, since

Q(m,pi(sqrt(m))) > pi(m), for m > 40291 .... [2]

You keep posting messages about "error in calculation".

But yours was an "error in understanding": the left

and right hand sides of [1] 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?

David