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

irrational prime products & sums

Expand Messages
  • WarrenS
    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))
    Message 1 of 1 , Feb 15, 2013
    View Source
    • 0 Attachment
      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 :)
    Your message has been successfully submitted and would be delivered to recipients shortly.