Search the first four billion binary digits of Pi for a string...  
Enter the string in hex (4 bit, 0-9A-F) or character (5 bit, a-z:;,_-.) format:



 

Assuming pi is normal, we have the following probabilities:
 
probability of occurrence for character
5 or fewer chars is ~100%
6 chars is 97.6%
7 chars is 11%
8 chars is 0.36%
9 chars is 0.01%
10 chars is 0.0003%

probability of occurrence for hex
7 or fewer digits is ~100%
8 digits is 60.6%
9 digits is 5.7%
10 digits is 0.36%
11 digits is 0.02%
12 digits is 0.001%



     In 1996, NERSC Chief Technologist David H. Bailey, together with Canadian mathematicians Peter Borwein and Simon Plouffe, found a new formula for pi.  This formula permits one to calculate the n-th binary or hexadecimal digits of pi, without having to calculate any of the preceding n-1 digits.  This formula was discovered by a computer, using Bailey's implementation of Ferguson's PSLQ algorithm.  More recently (2001), Bailey and colleague Richard Crandall of Reed College have shown that the existence of this new formula has significant implications for the age-old question: Are the digits of pi random?

Related links:
 
The 1996 paper with the new formula for pi.
The paper that discusses the significance of this new formula to the question of the randomness of the digits of pi and certain other constants.
An article in Science News (1 Sept. 2001, pg. 136) on the randomness paper.
A news article in Science (3 Aug. 2001, pg. 793) on the randomness paper.
 A new paper by Bailey and Crandall that proves normality (digit randomness) for a certain class of math constants.


Credits: David Bailey, concept and programming. Special thanks to Jed Donnelley, Victor Ruhle and Evan Welbourne for their help in the design and implementation of this tool, and especially to Yasumasa Kanada of the Univ. of Tokyo Computer Centre for providing us the first 4 billion binary digits of pi.

General Info/News | Computing Facilities | Research | Search
Table of Contents | Privacy and Security Notice | For Staff Only | Home