--- In

primenumbers@yahoogroups.com,

Jack Brennen <jfb@...> wrote:

> My guess is that it's a close miss, just because other known

> formulas for Pi such as the Wallis product are taken over all

> integers, not just over a subset of a subset of the integers.

We may also obtain Pi by taking products over primes,

having regard to their residues modulo 3 or 4:

prod(prime p > 2, 1 - if(p%4==1,1,-1)/p) = 4/Pi

prod(prime p > 2, 1 + if(p%4==1,1,-1)/p) = 2/Pi

prod(prime p > 3, 1 - if(p%3==1,1,-1)/p) = 2*sqrt(3)/Pi

prod(prime p > 3, 1 + if(p%3==1,1,-1)/p) = 3*sqrt(3)/(2*Pi)

What is hard to believe about Dimitris' numerology

is that he takes a residue-dependent product over

only /twin/ primes.

David