|p Statistics: Digit frequencies|
Doing a frequency analysis (FA) is nothing else but counting how many substrings of each possible pattern
appear in the complete digit sequence. For example: To analyze the substrings of length k=2 we read
the digit sequence in groups of digit pairs collecting every number into it's "home" box:|
14 -15 - 92 - 65 - 35 - 89 - 79 -32 - 38 - ...
In the end we will know how many "14", "15", "92" etc. were found.
This is the base for calculating the Chi2-value for the measured sequence to judge about p being random or not.
If p is RANDOM, each number "XY" should have an equal probability to appear.
|Digits analyzed: 4.2 * 10 9|
Analysis started at digit: 1
Ellapsed computer time for one class: 5 min - 7min 30 sec
|Length of |
|Number of different |
|Chi2||z-Value for |
|Why not testing longer sequences directly?|
There is a serious problem when testing the frequencies for longer and longer chains:|
We run out of data very fast.
When testing chains with L=8 on a 4.2 billion database we will get a poor expected average of 5.25 that is near the lower limit of Chi2 usage. One can calculate this average value by use of
A = N / (L x 10 L) where L is the length of proof sequences, N is the number of digits served to analyze.
Even when using the data of last calculation record of Yasumasa Kanada from october, 2002, with about 1.24 x 1012 digits we can just proof sequences up to k=10.
|More details of digit frequency analysis|
|For single digit frequencies|
|For double digit frequencies
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