Finally after years of discovering connections between PI and Scripture, I decided to create my own search engine for PI inspired by the original PI Search, that allowed searching the first 200 million digits of PI, and the Irrational Numbers Search Engine, which searched the first 2 billion digits of PI, as well as the Natural Logarithm – E, the Square Root of 2, and the Golden Ratio – Phi.

After a lot of trial and error coming up with my own optimized search (See Technical Details below), I added the first 10 billion digits of PI followed by 2 billion digits of other constants.

Findings

The number of significant connections that I have found between PI and other constants with Scripture, I could easily write a book. Here are couple of examples:

Constants

PI is probably the most important constant which I have found the most valuable results. The Twelfth root of 2 (musical frequency half-step) has become a new favorite. The Golden Ratio – Phi is found in nature and has also displayed valuable results as well as the Natural Logarithm – E, and the Square Root of 2.

To give you an idea just how accurate PI is at 32 digits, if the diameter was 1 light-year (9,460,730,472,580.800 kilometers), PI is accurate at the atomic level. Looking at the digits beyond 43 digits, the accuracy is beyond the atomic level of the observable universe. We are searching 10 BILLION digits of PI.

Experimental Constants

Currently, I am experimenting with the results of the Square Root of 3, the Lemniscate Constant, and the Euler-Mascheroni Constant. Since I am able to generate a few constants, I may be experimenting from time to time with some of the other constants that I am able generate. Some of the results seem promising, but there are hundreds, if not thousands of irrational numbers that will dilute the value of finding a significant result if they are all included in the search. For this reason, they need to be evaluated for a time to prove if the results have any value.

Other constants I would like to evaluate, such as cube roots, etc., but each takes time to generate to the accuracy of 2 billion plus digits.

Technical Details

I generated the data of each constant using y-cruncher, a multi-threaded program that generates PI and other constants to trillions of digits. In order to search through 10 billion digits of PI most efficiently, I first reduced the size of the data file in half by packing the ASCII digits that require 1 byte (8 bits) per digit into a nibble (4 bits) per digit. This reduces the amount of file I/O in half. Using the principles of the Boyer-Moore string search algorithm adapted to search a data source based on nibbles instead of bytes, I was able to reduce the search time even more. I replaced the main drives of my server with SSDs (Solid State Drives) and broke up the search into 32 simultaneous threads. This allowed me to find the last 12 digits of 10 billion digits of PI in 35 seconds. In comparison, the last 12 digits of 2 billion digits of PI took 7.959 seconds to find compared to the 16.2969 seconds from the Irrational Numbers Search Engine.

The final optimization was to create an 9 digit index of first positions in PI, and an 8 digit index of first positions for other constants. This allows me to return immediate results of all constants at once as long as the search is in the index. To search beyond the first occurrence or outside of the index, each constant is searched individually by request.

The Twelfth root of 2 required me to bumble my way through C++ code, and write my own NthRoot function with a program called Number Factory, and verified the accuracy with a verification file from here.