irrational prime products & sums
- Since you asked...
If F(n) is the nth Fermat prime, then
sum(n odd) 1/F(n)
sum(n even) 1/F(n)
product(n odd) (1-1/F(n))
product(n even) (1-1/F(n))
each are irrational... IFF there are an infinite number of Fermat primes
of the kind in that expression.
One must admit, though, that this is a pretty silly result, for
several reasons. I guess it is best posed as a puzzle, then :)