Pattern 97 Mathematical Constants Sampled Within Constants

Pattern Statement:

The first six digits of π, e, φ, and 2 sqrt ​ were searched for within the digit expansions of those same four constants. Each search selected six equally spaced digits using starting positions from 1 through 999 and intervals from 1 through 99.

Seven source-and-target matches were found:

π in π
e in π
2 sqrt in π
e in e
2 sqrt in e
e in φ
φ in φ

No qualifying match was found in the supplied digits of 2 sqrt ​ .

Why this pattern matters

This result illustrates that the opening digits of mathematical constants can sometimes be recovered by equally spaced sampling within other constants. The program uses the same defined search range for every source-and-target pair, allowing the complete result to be reproduced. This calculation is not derived from the words, letters, or Hebrew values of Genesis 1:1. It should therefore be treated as a related mathematical observation rather than independent evidence about Genesis 1:1.

How this pattern is measured

Four six-digit targets are defined:

Constant Target
π 314159
e 271828
φ 161803
2 sqrt ​ 141421

For each target and each of the four source constants, test every:

starting position from 1 through 999; and
interval from 1 through 99.

For a start s, interval d, and source digit string C, the selected sequence is:

C[s], C[s+d], C[s+2d],…,C[s+5d].

A result is reported when those six selected digits exactly equal the target.

Result for Genesis 1:1

7 matches among 16 source-target searches

Starts tested: 1–999 | Intervals tested: 1–99 | Target length: 6 digits
Source Target Start Interval Result
π π 195 4 314159
π e 965 58 271828
π 2 sqrt 149 3 141421
e e 513 71 271828
e 2 sqrt 600 44 141421
φ e 517 82 271828
φφ 430 36 161803

Read detail page for Pattern 97

Probability note

Each source-target search tests 999 × 99 = 98,901 equally spaced selections. Under a simplified independent random-digit model, the expected number of six-digit matches across all 16 source-target searches is:

16×98,901 over 10^6 ​ ≈1.58.

Seven matches were observed. A simple Poisson approximation gives a probability of approximately 0.0013, or roughly 1 in 800, of observing seven or more matches.

This estimate is approximate because the tested sequences overlap and are not fully independent. No additional probability is assigned to Bible verses found after interpreting the starting positions and intervals.

This page uses the probability notation provided in the original pattern sequence.

Supporting tables

2701 highlighted.

Although these tables relate to Genesis 1:1 and this pattern does not directly relate to Genesis 1:1, we have shown that Genesis 1:1 and universal constants are related. Therefore, we leave in these tables for continuity.
Genesis 1:1
Hebrew WordNumber of Letters
בראשית6
ברא3
אלהימ5
את2
השםימ5
ואת3
הארצ4
Total Words: 7Total Letters: 28
Traditional Hebrew Letter ValuesWord Total
2 200 1 300 10 400 913
2 200 1 203
1 30 5 10 40 86
1 400 401
5 300 40 10 40 395
6 1 400 407
5 1 200 90 296
Verse Value Total 2701
Hebrew Alphabet PositionsWord Total
2 20 1 21 10 22 76
2 20 1 23
1 12 5 10 13 41
1 22 23
5 21 13 10 13 62
6 1 22 29
5 1 20 18 44
Verse Position Total298