|p Statistics: Long Runs|
A LONG RUN (LR) is an uninterrupted line of a certain number in a digit sequence.
If the digit repeats itself M times it is also called an M-repeat. Testing LR is the opposite view to
the gap test which proofs nonoccurance.|
An M-repeat is a rare event because the probabilty to find exactly the same digit on the next place is 1/10 and so the chance for a LR falls down very quickly like 10-M.
When testing about 4 billion digits we will expect max long runs of 9 or 10 digits length.
A famous early LR in p is the FEYNMAN POINT at position 762 where a six digits repeat of "9" can be observed.
|Digits analyzed: 4.2 * 10 9|
Analysis started at digit: 1
Ellapsed computer time for each digit: 3 min 45 sec
|The estimated average LR-length is 1,111...|
Proofing the distribution for the entire number of LR's we found a Z-value for the normal distribution
Z = 1,8395.
|Table shows the Chi2-value of the LR distribution for each digit.|
The position of the 10 digits long runs are given additionally.
Download LongRuns-Details as an Excel file here.
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