A historical and computational corpus of the number 861

Volumes

1. 861 in the Tanakh · published
2. 861 in the Talmud and Midrash · published
3. Baal HaTurim · partial
4. Kabbalistic literature · partial
5. Bnei Yissaschar: תתס״א · partial
6. 861 and the Temple: בית המקדש · partial
7. 861 and Rosh Hashanah: ראש השנה · partial
8. 861 as a mathematical object · published
9. 861 × 354 · published
10. SAPIR 861: algorithm, data, API · published

Volume I. Words of the Tanakh summing to 861

Westminster Leningrad Codex (OSHB), CC BY 4.0 · Tanakh, 24 books · 306785 occurrences

Pairs of consecutive words in the Torah summing to 861: 42

Deuteronomy 4:19 — תשא עיניך · Deuteronomy 5:28 — אלי שמעתי · Deuteronomy 10:5 — שם כאשר · Deuteronomy 14:25 — וצרת הכסף · Deuteronomy 19:19 — לעשות לאחיו · Deuteronomy 29:21 — ואת תחלאיה · Deuteronomy 33:2 — מימינו אשדת · Exodus 28:40 — ועשית להם · Exodus 28:42 — ערוה ממתנים · Exodus 29:36 — תעשה ליום · Exodus 32:8 — מסכה וישתחוו · Exodus 39:29 — רקם כאשר

Triples of consecutive words in the Torah summing to 861: 47

Deuteronomy 5:5 — כי יראתם מפני · Deuteronomy 16:7 — בבקר והלכת לאהליך · Deuteronomy 17:2 — נתן לך איש · Deuteronomy 27:11 — משה את העם · Deuteronomy 28:57 — היוצת מבין רגליה · Deuteronomy 29:13 — הזאת ואת האלה · Deuteronomy 29:13 — ואת האלה הזאת · Deuteronomy 33:21 — מחקק ספון ויתא

Editions: what we found

The first step of the protocol is to find the edition and the scan. This shows where each source stands and on what terms it may be used.

We do not republish the scan: we cite the edition and the leaf and link to the repository. Next step — locate the leaf and do the manual recount.

First check against the leaf: the record is withdrawn

We downloaded the scan of the first edition of Sefer Karnayim (Żółkiew, ⁦תס״ט⁩ / 1709, National Library of Israel) and located the leaf: maamar ⁦יא⁩, the Dan Yadin commentary, pages 32–33 of the NLI file.

The leaf shows that the two expressions our database held as the left and right sides of an equality belong to one sentence.

ג׳ אותיות אלו: סע״ף — בגימטריא הכי הוי — מורה על יציאת מצרים

The gematria discussed there is ⁦סע״ף⁩ = 210. There is no equality yielding 862 on that leaf.

Why the record appeared at all: the extraction cut the sentence at the word “⁦בגימטריא⁩” and took what stood on either side. The sums matched by accident: “⁦ג אותיות אלו⁩” = 863, “⁦מורה על יציאת⁩” = 862 — a difference of one, so the row entered the database as “with kollel”.

Result: the only attestation for 862 is withdrawn. It is the same failure as in the 861 record — now named, and the pipeline gains a check: a sentence is not cut at the word “gematria”.

We do not republish the scan: the edition, the leaf and the repository are cited — anyone can verify.

Volume II. 861 in the Talmud and Midrash: what the search returned

In our corpus (Hebrew Wikisource, 834 works, CC BY-SA 4.0) there are exactly two attestations for 861, and neither is Talmudic or Midrashic. In other words: we found no Talmudic or Midrashic attestation of 861.

This is a result, not a gap. We publish it now, before a convenient quotation turns up — so that it cannot be inserted after the fact.

What would change the status: a printed edition with commercial-use rights, a scan of the page, a literal translation, a manual recount, and a check of independence from an earlier source. Until we have that, the line stays empty.

The computable part of this volume: in the whole Tanakh exactly one verse has a consonant sum of 861: Psalms 119:91

This is arithmetic and nothing else. We do not interpret the verse and build no claim on it.

The 54 words by book

Volume IV. Kabbalistic literature

Two works in the corpus touch the 861 band: Bnei Yissaschar (~1830) — an exact record, and Sefer Karnayim (~1400) — a record with kollel, and it belongs to 862, not to 861.

Kollel is an added unit. Tradition treats such a record as admissible; we treat it as a separate type: 861 and 862 never merge into one line here, and the difference is always labelled.

The volume's status is “partial”, and that is honest: the Kabbalistic section of Wikisource is incomplete, many works appear as late reprints, and we do not have edition and page for every record.

The ±1 band in the words of the Tanakh

Note: 354 words sum to 860 — the same number as the pages in “Chumash 354”. That is a coincidence of counters and nothing more; this is exactly what our detector flags.

Words of the Tanakh whose sum equals a divisor of 861

Attestations in the sources

Found in the corpus: 861 — two attestations, both exact, one work. Both records were extracted by machine and are undergoing manual verification.

The earliest in our corpus: בני יששכר מאמרי חודש כסלו טבת (~1830, טוב) — קרן השור = מתתיהו = 861 · unconfirmed, collation ongoing

862: 2 · ספר קרניים (~1400)

Verification result (23.09.2026): In Bnei Yissaschar, Maamarei Chodesh Kislev–Tevet, maamar ג, ot ד, a midrash is cited: «כתבו לכם על קרן השור: אין לכם חלק באלקי ישראל»; מתתיהו כהן גדול is mentioned in the same maamar (ot א). An explicit equation «קרן השור בגימטריא מתתיהו» was not found in the text available to us; the number תתס״א does not appear in it either.

What is needed: Collation against the printed Kislev–Tevet edition (folio, siman). Until that collation, the record is treated as unconfirmed: the extraction may have joined two adjacent expressions rather than the equation attributed to the author.

Corpus of attestations: Hebrew Wikisource, 834 works, CC BY-SA 4.0; extraction by our own code. 3,453 records from 20 works were checked line by line; the rest is aggregated and awaits verification.

Arithmetic and attestation are different things

בית המקדש = 861 — The letter sum matches, but no historical attestation has yet been found in our corpus. This does not mean there is none: it means we have not found it and do not present a match as a tradition.

ראש השנה = 861 — The letter sum matches, but no historical attestation has yet been found in our corpus. This does not mean there is none: it means we have not found it and do not present a match as a tradition.

מתתיהו = 861 — Both the sum matches and an attestation exists.

קרן השור = 861 — Both the sum matches and an attestation exists.

Volume III. Baal HaTurim

Jacob ben Asher, died before 1340, Toledo — «Rimzei Baal HaTurim», a commentary on the Torah: gematria, notarikon and masoretic counts, with almost no exposition

Constantinople, 1500

221 / 3138 · 166 + 54 ±1 · 1

The numbers 861 and 862 do not occur in Baal HaTurim. The earliest source for 861 in our database remains Bnei Yissaschar (~1830), and after the check in volume V its record is marked as unconfirmed.

157 of 221 expressions consist of several words — the same splicing risk as in volume V. Folio-level collation has not been carried out: Hebrew Wikisource is served only from cache, and hebrewbooks.org returns 403.

Quality of the database: recomputation of all records

Recomputation of all 1023 values in the attestation database using our own letter count.

1023 · 599 · ±1: 416 · 8

Eight records do not add up arithmetically. Seven of them are statements of the form «letter = name of the number» (א = אחד, ו = ששה, ט = תשעה): this is not a gematria equation but a number written out as a word, and such rows should not have entered the database. One record (999) is an extraction cut off mid-phrase.

A mandatory check is added to the pipeline: a row is accepted only if the sum of the left and right expressions equals the value (or differs by 1 with the note «im ha-kolel»).

Volume VIII. Mathematics

861 = T41 = 1+2+…+41

861 = 3 × 7 × 41

1 · 3 · 7 · 21 · 41 · 123 · 287 · 861

861 − 354 = 507 · 354 × 2 = 708 · 861 × 354 = 304 794

Volume IX. 861 × 354

354 × 861 = 304794

Binyamin Pichkhadze, «Chumash 354» (חומש 354), Bnei Brak, 2002

31 of 31 control pages match the edition

Open question: WLC — 304850, Reconciled 354 of 354 pages. WLC Torah consonants (ketiv) = 304,850; the 354×861 grid = 304,794. The 56-letter difference is fully accounted for: page 1 has 872 letters (+11), and 45 = 47 pages with one extra letter minus 2 pages with one fewer, where WLC spelling differs from the edition (304,805). Page table: /data/pages_861x354.csv

How we work with a source

1. Scan and folio of the edition.
2. Original Hebrew text.
3. Literal translation.
4. Manual recount of the letters.
5. Historical context of the work and its author.
6. What the source actually states.
7. What follows from it and what does not.
8. Independence: whether a later source merely repeats an earlier one.