module Main where{

import Data.List;

primes::[](Integer);
primes = (2:eratosthenes_sieve);
eratosthenes_sieve::[](Integer);
eratosthenes_sieve = (filter by_eratosthenes (enumFrom 3));
by_eratosthenes::Integer->Bool;
by_eratosthenes x = (and (map (indivisible x) (takeWhile (lt_sqrt x) primes)));
lt_sqrt::Integer->Integer->Bool;
lt_sqrt x p = ((<=) ((*) p p) x);
indivisible::Integer->Integer->Bool;
indivisible big small = ((/=) 0 (mod big small));


powers_of :: Integer -> [Integer];
powers_of x = x:(map (x*)(powers_of x));

largest_power_less_than :: Integer -> Integer -> Integer;
largest_power_less_than maxx x = let {
 l :: Integer -> Integer;
 l accum = case (x*accum <= maxx) of {
      True -> l (x*accum);
      _ -> accum
                                  }
  } in l 1;
           

primesmax :: Integer -> [Integer];
primesmax maxx = let {
  p1 :: [Integer];
  p1 = takeWhile (\x -> x<=maxx) primes;
  } in map (largest_power_less_than maxx) p1;


growing :: [[Integer]];
growing = map head $ group $ (map primesmax (enumFrom 2));

pr1 :: [Integer] -> IO ();
pr1 x = do {
          putStr (show ((sum(map ((log::(Double->Double)) . fromInteger) x))/(log 2.0)));
                 putStr " ";
          print ( x);
        };
                 

logp :: Integer -> Double;
logp x = log (fromInteger x);

main:: IO ();
main=mapM_ pr1 growing;
}