DouKaku?

require "mathn"
N=10
def meertens(n)
  prime = Prime.new
  primes = Array.new(n+1){prime.next}
  prime_list = primes.collect{|i| Array.new(10){|j| i**j}}
  result = Array.new
  goedel = 1
  n.times{|d|
    s = 10**d
    e = s*10 - 1
    s.upto(e){|i|
      if i%10 == 0
        k = 0
        goedel = 1
        i.to_s.each_byte{|j|
          goedel *= prime_list[k][j-48]
          break if goedel > i
          k += 1
        }
      else
        next if goedel > i
        goedel *= primes[d]
      end
      result << i if goedel == i
    }
  }
  puts result
end
meertens(N)