About 16.7 MKeys/s, 1 GKeys/min.
Let's say 2^24 Keys/s.
To compute 2 lists of 2^28 keys, it takes 2 * 2^4 seconds, about 30 seconds. That is the time it took to retrieve the key #57.
Have you tried to search a key in space of 10 quadrillion? How many hours you think it can finish that large space?
American or British system ? ->
https://www.quadrillion.com/number.shtmquadrillion = 10^15 -> 10 quadrillion = 10^16? 10^16 = 2^53 --> 2 lists of 2^26 keys = 2 * 2^2 = 8 seconds
quadrillion = 10^24 -> 10 quadrillion = 10^25? 10^25 = 2^83 --> 2 lists of 2^41 keys ? NO! Too much for my RAM!
Let's say that the max list size (for my RAM) is 2^28 keys.
To retrieve the #59, I need to compute 2 list of 2^29, I have to split the first in 2 * 2^28, then generate the 2^29 keys of the second list 2 times against each half of the first, tot: 2*2^28 + 2*2^29 = 3*2^29 instead of 2*2^29 (
96 seconds instead of 64 seconds).
To retrieve the #61, I need to compute 2 list of 2^30, I have to split the first in 4 * 2^28, then generate the 2^30 keys of the second list 4 times against each quarter of the first list, tot: 4*2^28 + 4*2^30 = 5*2^30 instead of 2*2^30 (
320 seconds instead of 128 seconds).
To retrieve the #63, I need to compute 2 list of 2^31, I have to split the first in 8 * 2^28, then generate the 2^31 keys of the second list 8 times against each part of the first list, tot: 8*2^28 + 8*2^31 = 9*2^31 instead of 2*2^31 (
1152 seconds instead of 256 seconds).
To retrieve the #65, I need to compute 2 list of 2^32, I have to split the first in 16 * 2^28, then generate the 2^32 keys of the second list 16 times against each part of the first list, tot: 16*2^28 + 16*2^32 = 17*2^32 instead of 2*2^32 (
4352 seconds instead of 512 seconds).
Time is for the
#(57+x) = (2^(x/2)+1) lists of 2^((57+x-1)/2) keys instead of only 2 lists of 2^(57+x-1)/2 keysFor the
#61 = #(57+4) = (2^2+1) * (2^30) = (2^2 + 1) lists of 2^30 -> 5 * 2^6 seconds = about 320 seconds =
5 min 20 secFor the
#71 = #(57+14) = (2^7+1) * (2^35) = (2^7 + 1) lists of 2^35 -> 2^7 * 2^11 seconds = about 2^18 seconds =
73 hoursFor the
#83 = #(57+26) = (2^13+1) * (2^82/2) = (2^13 + 1) lists of 2^41 -> 2^13 * 2^17 seconds = about 2^30 seconds =
34 years (if I had enough RAM, 2 * 2^41 = 2^42 keys = 2^18 seconds =
73 hours !!! I would need a RAM: 2^13 = 8000 times 32 GB)
ref: doh! eureka moment.