8,629 ATTESTATIONS · 834 WORKS · 12TH–20TH CENTURIES

One in four equalities needs a tolerance

When a 13th-century author writes “this equals that”, does it? We machine-recomputed 8,629 gematria claims from 834 works. Three in four hold exactly.

75.3%

6,494 of 8,629 attestations hold with no adjustment. The remaining 2,135 — 24.7% — need im hakolel: plus or minus one. This is not an error of the tradition; it is its tolerance, and nobody had measured it before.

The most frequently counted numbers

Value	Attestations	Works
86	155	57
13	154	56
65	129	45
345	127	45
72	110	51
110	106	20
12	104	69
52	97	53
45	92	42
70	90	44

Numbers that rarely hold without the adjustment

Value	Attestations	With adjustment	Share
110	106	90	85 %
67	23	14	61 %
161	22	11	50 %
74	22	11	50 %
31	37	17	46 %
6	22	10	45 %
111	39	15	38 %
346	33	12	36 %

Especially 110: of 106 attestations, 90 rest on the adjustment alone. The equality the tradition repeats most often is almost always one with a tolerance.

When a number was first recorded

Century	Values first recorded
XII	5
XIII	39
XIV	251
XV	182
XVI	212
XVII	58
XVIII	119
XIX	35
XX	8
XXI	1

For each of the 1,023 values, the earliest attestation found. Two peaks: the 14th century and the 16th. Dates of works are approximate, so this is a picture, not a chronometer.

Counting rule

Mispar hechrachi: alef 1 … tav 400, final letters equal to the ordinary ones, vowel points removed. “Exact” — both sides equal. “With adjustment” — a difference of exactly 1. Every row recomputed by machine; the CSV is open.

Download the database (CSV): value, attestations, exact, with adjustment, works, earliest

SAPIR 861 (2026). One in four classical gematria equalities needs im hakolel: 8,629 attestations from 834 works. Dataset. https://sapir861.com/research/kolel · DOI 10.5281/zenodo.22848828

The other study: Coincidence is cheap · /method · /research/spec

SAPIR 861 · sapir861.com · we count, we do not guess
Dataset CC BY 4.0. Text and morphology © Open Scriptures, CC BY 4.0. Attestations rebuilt from the Hebrew Wikisource (CC BY-SA 4.0) with our own code.

Value	Attestations	Works
86	155	57
13	154	56
65	129	45
345	127	45
72	110	51
110	106	20
12	104	69
52	97	53
45	92	42
70	90	44

Value	Attestations	Works
86	155	57
13	154	56
65	129	45
345	127	45
72	110	51
110	106	20
12	104	69
52	97	53
45	92	42
70	90	44

Value	Attestations	Works
86	155	57
13	154	56
65	129	45
345	127	45
72	110	51
110	106	20
12	104	69
52	97	53
45	92	42
70	90	44