Table 6 For the specious randomness file based on a single 25-bit number system, the probability to get some value a, lower than the cumulative distribution function Eq. (19) is tabulated for different n-grams ≤25, using non-overlapping (column 2) and overlapping (column 3) counting of n-grams. We know that for \(n=1,5\) and 25, all n-grams occur equally frequently, therefore the sequence is skip-balanced for those n-values
n | \(P(2^{n}-1,a\leq \chi ^{2}_{1})\) (non-overlapping) | \(P(2^{n}-1,a\leq \chi ^{2}_{2})\) (overlapping) |
|---|---|---|
1 | 0 | 0 |
2 | 0.62 | 0.0061 |
3 | 0.020 | 0.000085 |
4 | 0.067 | 0.000000037 |
5 | 0 | 0.00000000010 |
6 | 0.37 | <10−15 |
7 | 0.048 | <10−15 |
8 | 0.012 | <10−15 |
9 | 0.18 | <10−15 |
10 | <10−15 | <10−15 |
11 | 0.010 | <10−15 |
12 | 0.0026 | <10−15 |
13 | 0.11 | <10−15 |
14 | 0.000025 | <10−15 |
15 | <10−15 | <10−15 |
16–25 | <10−10 | <10−15 |