= 3.14159...

Search 2 x 109 decimal digits of Pi, E, the Square Root of Two and 5 x 108 digits of Phi (the Golden Ratio) for the first occurrence of a numeric string, or display a specified number of digits from a given starting position.

Enter digits to search or start position:
Mode: Search
Display digits from start position
Constant: Pi
Sqr Root 2
Phi (500M)


Please enter a numeric string to search or a starting position (decimal digits only)

About the Irrational Numbers Search Engine:

Why create an irrational numbers search engine? Why not! Built in 2002 just for fun, the original implementation only offered digits for Pi and ran on a makeshift server in my basement. The hardware has since been continually upgraded and the application tuned for performance. Digits for Euler's Number, Phi and the Square Root of 2 were added in 2011 by popular request.

Usage has steadily increased over time, with 948,457 searches processed in the 5 years between 2010 and 2014. Usage spiked dramatically in 2013 with 301,050 searches, and tapered off slightly in 2014 with a total of 261,826. As of June 2015, the search engine is processing an average of 40K queries per month, indicating a recent uptick in usage!

Search History Search Types
Search Totals Searches by Type

Between 2010 and 2014, 14,440 unique visitors from 116 countries accessed the search engine, including numerous corporations, universities and schools across the globe. I have received a range of user feedback, citing uses spanning research (from the mainstream to the fringes of credibility) to Geocachers who have used the site to embed clues within the digits of Pi. It has been interesting and rewarding to see the variety of 'uses' for the search engine!

Search Locations Search Locations
Top Countries Searches by Continent

Searches during this period averaged 6.6 digits, with an average search time of 1.91 seconds. CPU time totaled 1,694,826 seconds, or over 470 hours!

How it works:

The search engine was originally implemented as a VB6 executable invoked within a shell command by an ASP page, using text files for input and output. That approach was a bit of a kludge, so I rewrote it as a VB6 class (.dll) callable from within an ASP page. You can download the VB6 source code, executables and sample VBScript code here. The source code package has been downloaded 1,962 times as of 6/1/2015.

Digits for each constant are contained in ASCII text files using one byte per digit and a full scan of a 2GB file completes in under 15 seconds.  The application runs on a Windows Server virtual machine hosted on a 2011 Mac Mini Server.  The VM is allocated 8GB of RAM which enables disk I/O caching for all search files and therefore excellent throughput and concurrency.  The search engine currently supports 4 concurrent searches, which is a function of the number of CPU cores available to the virtual machine.

Send us a note about how you're using the search engine using the contact us link below - any comments, suggestions or ideas are welcome!


Pi, e, the Square Root of 2 and the Golden Ratio (Phi) on Wikipedia
10,000 decimal digits of Pi, E, SqrRt2 and Phi
Pi, E, the Square Root of 2 and Phi digits calculated using PiFast43 written by Xavier Gourdon.
The *original* Pi Search Engine that inspired this one; much faster, but only 200m digits. Good background and statistical info.
National Energy Research Scientific Computing (NERSC) Pi Search Page
Online Encyclopedia of Integer Sequences references to this site: https://oeis.org/A232013 and https://oeis.org/A232014

The search engine has processed 1,330,030 queries since 01/09/2002
0 searches currently active

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