>> So with a 10TH miner you can try 10^13 / 10^5 = 10^8 passwords per second ...'
This ignores the intolerable overhead created by the computer you are trying to hack!
If the remote is deliberately imposing a 1 second turnaround to verify. Using your 10^8 password attempts. The situation is thus:
10^8/seconds/minutes/hours/days/365
10^8/60/60/24/365 = 3.17 years of overhead that the attacking computer has no control over. Your computer speed is of no consequence.
Assuming that your quantum magic computer might chew 10^8 permutations in one second. That still means 3.2 years + one second to do the job.
Of course, you might get lucky and strike gold after the first 8 months.
Or you can attack 100 different computers at once improving the chances of a single successful hit in a shorter period of time.
But the fact remains I think the "Hive Systems" chart is a fantasy designed to scare you into using their services.
Did I forget to mention that any good password verification will lock you at after 3 or 5 failed attempts? Now we're talking centuries to crack any good password.