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Pattern 74 Three Subset Strings Reach Divisibility by 37 at Offsets 0, 1, and 2

Pattern Statement:

Pattern Statement: For every nonempty subset of letters within each word of Genesis 1:1, three numbers are calculated from the subset’s traditional Hebrew value and alphabet-position value:

value − position, value + position, and value.

These numbers select digits from π, producing three 157-digit strings. The first string is divisible by 37 with no offset, the second first becomes divisible by 37 at offset 1, and the third first becomes divisible by 37 at offset 2—the earliest possible ordered result.

Why this pattern matters

Each of the three independently constructed strings reaches divisibility by 37 at its corresponding earliest offset:

Value − position: offset 0
Value + position: offset 1
Value: offset 2

Their offset total is therefore 0 + 1 + 2 = 3, the minimum possible total when the three required offsets are 0, 1, and 2 respectively.

How this pattern is measured

The seven words of Genesis 1:1 contain 28 letters. Subsets are formed separately within each word; a subset never crosses a word boundary. Every nonempty letter subset is included.

For word lengths 6, 3, 5, 2, 5, 3, and 4, the number of subsets is:

(2⁶−1) + (2³−1) + (2⁵−1) + (2²−1) + (2⁵−1) + (2³−1) + (2⁴−1) = 63 + 7 + 31 + 3 + 31 + 7 + 15 = 157.

For each subset:

Calculate its traditional Hebrew value. Calculate its Hebrew alphabet-position value. Calculate value − position, value + position, or value. Add the decimal digits of that result. Use the resulting number, plus the tested offset, as an index into the digits of π. Append the selected digit to the corresponding 157-digit string. Test the completed string for divisibility by 37.

For each of the three methods, offsets are tested in order from 0 through 36, stopping at the first divisible string.

Result for Genesis 1:1

Value − position: first divisible by 37 at offset 0
Value + position: first divisible by 37 at offset 1
Value: first divisible by 37 at offset 2

Offset total: 0 + 1 + 2 = 3

1 | 0 1 2 | 3 FOUND

groups.java does not simply test “random strings.” For each control trial, it:

shuffles the existing letters separately within each Genesis 1:1 word, preserving all seven word lengths and letter inventories;

replaces π with a newly generated 70,000-digit pseudorandom decimal sequence;

repeats the same subset and divisibility procedure;
uses a fixed seed, defaulting to 73, so the run is reproducible.

Control test: The program performs 99,999 control trials after testing Genesis 1:1. Each trial preserves the seven word lengths and the letters belonging to each word, but shuffles their order and substitutes a pseudorandom digit sequence for π. A control counts as a match only if its three first successful offsets are exactly 0, 1, and 2.

Genesis 1:1: 0, 1, 2 — FOUND
Matching controls: 0 out of 99,999

37 found

Read detail page for Pattern 74

Probability note

No control trial reproduced the complete ordered result in 99,999 trials. Therefore, the empirical test found a frequency of 0 out of 99,999, rather than establishing an exact probability.

As a simple theoretical comparison, if each first successful offset were uniformly and independently distributed among 0 through 36, the probability of the specified ordered result 0, 1, 2 would be approximately:

(1/37)³ = 1/50,653.

This estimate does not account for the selection of the three formulas, π, subset ordering, or the target number 37.

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

The tables provide the traditional value and alphabet-position value used for every Hebrew letter. All 157 nonempty within-word subsets are generated from these entries.

Supporting tables

Letter values and places are highlighted.

Genesis 1:1
Hebrew Word	Number of Letters
בראשית	6
ברא	3
אלהימ	5
את	2
השםימ	5
ואת	3
הארצ	4
Total Words: 7	Total Letters: 28

Traditional Hebrew Letter Values						Word 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 Positions						Word 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 Total						298

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