p Statistics: Long Runs |

by JVSchmidt |

General considerations | ||

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. |

Results | ||||||||||||||||||||||||||||||||||||||||||||

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 Chi^{2}-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. <= Back to Main |