I have 20 digit, uniformly distributed random numbers, downloaded from random.org (because the numbers from that source are based on variations in atmospheric pressure rather than a mathematical algorithm).
Random.org has a daily limit on free downloads.
I seek reasonable and ideal ways to use the 20 digit numbers to form multiple, shorter, 5 digit independent random numbers. (The length of 5 is somewhat arbitrary.)
For the sake of this question, let's represent the digits of a 20 digit number by the first 20 letters of the alphabet:
Clearly I could split each 20 digit random number into 4 independent random numbers, say the first 5 digits, the second 5 digits, etc., like this:
abcde fghij klmno pqrst.
The question is: Can I get more than 4 independent 5 digit random numbers from each of the 20 digit numbers and, if so, how many?
Clearly, I can NOT do this to form 16 shorter numbers:
abcde bcdef cdefg defgh efghi etc.
Adjacent pairs of these numbers correlate about .1. (Don't ask how I know that.)
But consider this approach to get 6 independent random numbers from each 20 digit number:
abcde defgh ghijk jklmn mnopq pqrst
Would these 6 numbers be independent, random numbers, at least for all practical purposes??
If I can reasonably form more than four 5 digit random numbers from the original 20 digit numbers, what is the maximum number of 5 digit numbers that could be formed and still be independent, at least for all practical purposes?
Or am I better served by simply dividing the 20 digit numbers into 3 digit random numbers, yielding almost 7 shorter numbers, and avoid the complexities of the long question above?