--- In firstname.lastname@example.org
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.