Longest chain of digits in $\pi$.

Question

What is the longest chain of same digits in $\pi$?

This question comes into my mind while reading about the Feynman Point in a book. So is there any longest known chain? Like $999999$ of Feynman point.

Pretty sure that no one knows the answer. If $\pi$ is normal like it is conjectured to be, then there is no longest chain. — Dylan, Nov 12 '15 at 07:15
I mean just like Feynman point, are there similar chains known uptill or those six $9$s are the longest? — Kushal Bhuyan, Nov 12 '15 at 07:18
Play with http://www.angio.net/pi/piquery.html. You will see — Claude Leibovici, Nov 12 '15 at 07:24
If the decimals are truly random, as they seem to be, then any sequence of digits of length K appears every 10^K digits on average, without any limitation on K. — , Nov 12 '15 at 13:55

score 7 · Accepted Answer · edited Nov 24 '22 at 17:58

Playing on this site, I reproduced below the longest string of repeated numbers, the position and number of times they appear in the first 200 million of digits of $\pi$

 00000000  172330850  2
 11111111  159090113  3 
 22222222  175820910  1 
 33333333   36488176  1 
 44444444   22931745  2 
 55555555  168743355  1 
666666666   45681781  1 
777777777   24658601  1 
888888888   46663520  1 
 99999999   66780105  1

The problem is that 200 million is quite small when compared to the 12.1 trillion digits available since December 2013.

Have a look at this page for more impressive answers.

Taken from Fabrice Bellard page (2.7 trillion digits), the longest repetitions (digit, length, position); this is much more impressive than with the poor 200 million digits.

0  12  1755524129973
1  12  1041032609981
2  12  1479132847647
3  12  1379574176590
4  12  1379889220413
5  12  1618922020656
6  12  1221587715177
7  12   368299898266
8  13  2164164669332
9  12   897831316556

Longest chain of digits in $\pi$.

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