moge.rb

def primes_to(x, ns = 2.upto(x).to_a, ps = [], to = Math.sqrt(x))
  ns.first.tap { |p| break p.nil? ? 0 : p > to ? ps + ns : primes_to(x, ns.reject{ |n| n % p == 0 }, ps << p) }
end

def prime_count x
  primes_to(x).size
end

[2, 5, 10, 19, 54, 224, 312, 616, 888, 977, 1000000].each do |x|
  p prime_count(x - 1)
end