Loading ...
Sorry, an error occurred while loading the content.

24877irrational prime products & sums

Expand Messages
  • WarrenS
    Feb 15, 2013
      Since you asked...
      If F(n) is the nth Fermat prime, then

      sum(n odd) 1/F(n)
      and
      sum(n even) 1/F(n)
      and
      product(n odd) (1-1/F(n))
      and
      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 :)