--- In

primenumbers@yahoogroups.com,

"djbroadhurst" <d.broadhurst@...> wrote:

> m*prod(k=1,pi(sqrt(m)),1 - 1/prime(k)) + n - 1 = pi(m) ... [1]

> It is rather easy to prove that the number of solutions to [1]

> is finite, in direct contradiction to a conjecture by Sergey.

It is interesting to see how Sergey fooled himself into

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

http://tech.groups.yahoo.com/group/primenumbers/message/20936?var=0
prompted Mike Oakes' impressive statistics in

http://tech.groups.yahoo.com/group/primenumbers/message/20940?var=0
David