In explaining how hard it is to crack the code of the Enigma machine, Cumberbatch' character says in The Imitation Game:
There are 159 million, million, million possible Enigma settings. All we had to do was try each one. But if we had 10 men checking one setting a minute for 24 hours every day and seven days every week, how many days do you think it would take to check each of the settings? Well, it’s not days; it’s years. It’s 20 million years. To stop an incoming attack, we would have to check 20 million years’ worth of settings in 20 minutes.
For no reason other than curiosity, I tried to calculate whether or not this "20 million years" is correct, and found that it is completely incorrect.
Let's just use simple math to do this: It's stated that the Enigma machine has 159 million million million different settings, that's 1.59×10^20. Let's assume that a man can check a code each second (which is much faster than what was stated in the movie), and while a year has 31,536,000 seconds, then in 20 million years period that would be: 10(men)× 31,536,000(seconds in a year) × 20 ×1,000,000 (20 million years) = 6.3×10^15 settings. Obviously that is so much less than the Enigma settings so there is a huge error in saying "20 million years" as it would take much much longer than that. 25,000 times more to be precise.
So is this a calculation mistake they made?