"Throughout the many centuries pi (π) has been examined and dissected in countless ways. The fascination with pi continues to the present. To this day no one has noticed anything unusual about pi.
When I was eighteen years I noticed the 3_4_5 right at the start of pi. I thought it odd that the Pythagorean triplet would begin right at the start of pi but gave it no more thought. Years later I noticed the 1_1_2 at the start of the square root of two and thought that this discovery was strange. These two oddities both at the same position fanned my curiosity. During the many years of examining pi (π), √2 and S I found that these three constants have an very odd interwoven relationship.
[..]Pi = 3.14159265358979323... It is very odd that a group of eight small different contiguous primes: 3, 14159, 2, 653, 5, 89, 7, 9323 are right at the start of pi. Many and possibly infinite small (numbers with five or fewer digits) and large (greater than five digits) different contiguous primes may exist after 9323. As it turns out right after the 9323 prime the next contiguous prime is: 846264338327........303906979207, it is 3057 digits long. So if pi started with 8462... the first prime would be 3057 digits long.
It will be interesting to see how many digits the average contiguous prime has. Perhaps more interesting may be to find how scarce are groups consisting of eight small contiguous primes of which none of the prime numbers are duplicated."
~~Extracts taken from "Proof of the Existence of God - The Ingenious Numeration of Three Constants" by Vasilios Gardiakos http://www.artmusicdance.com/vaspi/highlights.htm