Re: Number of prime numbers between the values of (m) (m1)
- --- In email@example.com,
"djbroadhurst" <d.broadhurst@...> wrote:
> m*prod(k=1,pi(sqrt(m)),1 - 1/prime(k)) + n - 1 = pi(m) ... It is interesting to see how Sergey fooled himself into
> It is rather easy to prove that the number of solutions to 
> is finite, in direct contradiction to a conjecture by Sergey.
making his false conjecture. His mistake was to believe
that we may rely on the sieve of Eratosthenes to give
the "right" constant in the prime number theorem. In fact,
we should not: there is a mismatch by the celebrated factor
2*exp(-Euler) > 1 that so perplexed Pafnuty Lvovich Chebyshev
and Franz Carl Joseph Mertens.
Elsewhere in this list, one may find an investigation of this issue.
In particular, my remarks in
prompted Mike Oakes' impressive statistics in