Ok but how you image to work with bigger size of range, the nearest 2**130…? How much ram do you need to generate such equation ?
I don't image to work with bigger size of range.
At this level the problem in my opinion is to shrink the size of database. That's all.
To "cover" a 2**130 space, you need 2**65 keys with distance 2**65.
2**65 keys with 128 bits (at least) for each key means 2**73 bit = 2**70 bytes, 1 Billions of TB.
If you use the script of the OP, 2**65 keys = 2**65 bits = 2**62 bytes = 4 Millions of TB.
These are the numbers.
These script are made for fun, not to become rich.
Although your numbers are correct, you forget about statistics and probabilities.
because when you involve chance, the larger your sample, the larger your probabilities are, so when you sacrifice your sample size for speed, it can serve you well in small ranges but in high ranges the number of probable objects you can hit is always better.
An example in the real world is rain, if the speed at which the water fell to the ground was double, it would wet less space on the earth, the drops would be larger.
The fewer raindrops = the greater the proportion of dry soil.
It's just the big problem with bsgs.