mech.rb

require 'mechanize'
require "prime"

agent = Mechanize.new
primes = Prime.new
pr = primes.next

results = []

while (pr <= 1000) do
  pr = primes.next

  agent.get("http://wolframalpha.com")
  form = agent.page.forms.first
  form.i = "1/#{pr}"
  form.submit

  v = agent.page.search("#i_0400_1").first.attributes["alt"].value
  if v =~ /period/
    results << [pr, v.scan(/period \d+/).first.gsub("period ", "").to_i]
  end
end

puts a.max { |a, b| a[1] <=> b[1] }