> if 2^512 calculations costs you $8 then (2^512)^2 calculations costs you $64
Can you answer
a) If 1 apple costs you 8$ then (1)^2 apple costs you: ???
b) If 10 apples cost you 8$ then (10)^2 apples costs you: ???
edit: between the price and the amount, usually there is a ~linear relationship. So if you can buy 2^512 something for 8$, then chances are that for 8 times the price you'll only get ~8 times more amount, and not 2^512 times more
The tldr is bigO gives you how the cost of apples changes with the number of apples in the worst case.
its a rough simplification, the precise formula is close but not exactly that. the simplification is also actually (2n)^2 but in my defense I was going from memory of work from more than 2 decades ago (testing generated prime factors were good prime factors, overwhelmingly they were not).
using your apples example
if the bigO of eating apples is O(n^2), and it takes you 8 minutes to eat 2 apples, it will take you no more than 64 minutes to eat 4 apples.
Can you answer
edit: between the price and the amount, usually there is a ~linear relationship. So if you can buy 2^512 something for 8$, then chances are that for 8 times the price you'll only get ~8 times more amount, and not 2^512 times more