The Abjad Sum 1327 of the Ten Most Frequent Quranic Word Forms

Abstract

QMR-008 reconstructs a 2025 observation concerning the ten most frequent exact word forms in the Quranic text.

Under the recovered TRAD_T1 Mashriqi Abjad table, those ten forms have values whose sum is:

1327

The deterministic result survives reconstruction on the canonical DATA-001 corpus in both RAW and BODY views. The same ten exact forms occupy the first ten frequency ranks in both views, and their TRAD_T1 sum remains 1327. The number 1327 is prime and is the 217th prime.

The historical record also contained several errors that do not survive reconstruction: the displayed 2025 frequencies summed to 23,250 rather than 24,252; 1327 is not the 216th prime; and its base-12 representation is 927, not the claimed palindromic 931.

Two further challenges materially limit the interpretation. First, a defined orthographic normalization changes the sum from 1327 to 1339 = 13 × 103, removing primality. Second, a seeded one-million-permutation challenge finds that prime sums occur in roughly 12% of comparable randomizations under the tested null models. The primality of 1327 is therefore reproducible as an arithmetic observation but is not statistically unusual under those models.

QMR-008 is consequently classified as an E1 structured observation, not as statistical evidence and not as a discovery.

Research Question

QMR-008 asks two separate questions:

1. What is the TRAD_T1 Abjad sum of the ten most frequent exact orthographic word forms in DATA-001?
2. Is the property “the top-10 sum is prime” statistically unusual under explicit null models?

The deterministic and statistical questions are treated separately.

Historical Record

The recovered 2025 record listed the following ten forms:

من · الله · في · ما · إن · لا · الذين · على · إلا · ولا

The historical frequency values were:

Those ten displayed values sum to 23,250, not 24,252.

Separate recovered notes also show that older analysis pipelines could assign different counts to the same lexical item. For example, من was recorded as 5,253 in the historical word_analyzer output and 2,763 in another extraction path. QMR-008 therefore does not reuse the old counts as modern exact-token frequencies.

Corpus and Counting Rule

The modern reconstruction uses DATA-001:

• Tanzil Quran Text — Simple Clean — Version 1.1
• 114 surahs
• 6,236 verse identifiers
• RAW: 78,248 whitespace-delimited words and 332,837 Arabic letters
• BODY: 77,800 words and 330,709 letters

The canonical DATA-001 SHA-256 is:

228DF2A717671AEB9D2FF573002BD28D6B3F973F4BC7153554E3A81663D67610

For QMR-008, a word form means an exact whitespace-delimited token. No Unicode or orthographic normalization is applied before frequency counting.

BODY removes the exact four-token opening Basmala prefix from the first verse of 112 eligible surahs while leaving S1:1 and S9:1 unchanged.

Recovered TRAD_T1 Abjad Convention

The recovered historical table is:

TRAD_T1 is applied literally to these 28 defined characters. Characters absent from the recovered table contribute zero in the historical implementation.

This convention explains the historical values directly. For example:

• من = م40 + ن50 = 90
• الله = ا1 + ل30 + ل30 + ه5 = 66
• إن = ن50 = 50 because إ is outside the literal recovered table
• على = ع70 + ل30 = 100 because ى is outside the literal recovered table

The Abjad numerical use of Arabic letters is historically established; see Georg Krotkoff, “ABJAD,” Encyclopaedia Iranica.

Deterministic DATA-001 Result

The modern exact-token ranking is:

The rank order is identical in RAW and BODY.

The Abjad sum is:

90 + 66 + 90 + 41 + 50 + 31 + 791 + 100 + 31 + 37 = 1327

Therefore:

RAW top 10 → 1327 → prime

BODY top 10 → 1327 → prime

1327 is the 217th prime.

The ten exact forms account for:

• RAW: 11,806 / 78,248 = 15.0879% of tokens
• BODY: 11,694 / 77,800 = 15.0308% of tokens

The RAW/BODY difference is internally consistent. الله decreases from 2,265 to 2,153, a difference of exactly 112, matching the 112 removed Basmala prefixes.

Corrections to the 2025 Record

The reconstruction supports the core 1327 arithmetic observation but corrects several associated claims.

Confirmed

• the same ten forms are the exact top ten under DATA-001 RAW;
• the same ten forms remain the exact top ten under DATA-001 BODY;
• their literal TRAD_T1 sum is 1327;
• 1327 is prime.

Corrected

• displayed historical frequency sum: 23,250, not 24,252;
• modern exact-token top-10 total: 11,806 RAW / 11,694 BODY;
• corpus share: approximately 15.09% RAW / 15.03% BODY, not 31.21%;
• prime rank: 217th, not 216th;
• base 12: 1327₁₀ = 927₁₂, not 931;
• therefore the claimed base-12 palindrome does not reproduce.

Not recovered as valid inference

The 2025 probability claim of approximately 2.3 × 10^-6 was not accompanied by a recoverable null model, seed, permutation count, multiple-testing correction, or pre-specified inferential target. It is not retained as a valid statistical result.

Orthographic Sensitivity

A sensitivity analysis normalizes only:

• إ → ا
• ى → ي

before applying the same 28-letter table.

Under that alternative rule:

• إن: 50 → 51
• على: 100 → 110
• إلا: 31 → 32

The top-10 sum becomes:

1339 = 13 × 103

and is therefore not prime.

The observed primality is consequently convention-sensitive. The defensible statement is that 1327 is prime under the explicitly defined recovered TRAD_T1 convention, not under every plausible orthographic normalization.

Statistical Challenge

The primary exploratory metric was frozen as:

whether the cumulative TRAD_T1 Abjad sum of the exact top-10 word forms is prime.

The challenge used:

• 1,000,000 permutations
• base seed 20260917
• RAW as the primary corpus view
• BODY as a sensitivity view
• top-k sensitivity from k = 5 through k = 20

Two null models were evaluated.

Global reassignment null

TRAD_T1 values are randomly reassigned across exact word forms while the top-frequency rank positions are held fixed.

For RAW top 10:

• prime outcomes: 117,589 / 1,000,000
• prime rate: 11.7589%
• Wilson 95% interval: approximately 11.696%–11.822%

For BODY top 10:

• prime outcomes: 117,928 / 1,000,000
• prime rate: 11.7928%

Length-matched reassignment null

TRAD_T1 values are reassigned only among exact word forms with the same Unicode code-point length, preserving the length profile of the ranked top forms.

For RAW top 10:

• prime outcomes: 123,992 / 1,000,000
• prime rate: 12.3992%
• Wilson 95% interval: approximately 12.335%–12.464%

For BODY top 10:

• prime outcomes: 125,168 / 1,000,000
• prime rate: 12.5168%

Under both tested null models, a prime top-10 sum occurs on the order of one time in eight to nine trials. The property “the sum is prime” is therefore not statistically unusual under these models.

Exact-1327 Diagnostic Is Post Hoc

The same Monte Carlo runs also recorded how often the randomized sum equaled exactly 1327.

Those rates were much smaller than the general prime rates. However, 1327 was already known before the challenge was designed.

Selecting the exact observed value after seeing it creates a post-hoc target. These exact-1327 frequencies are therefore descriptive diagnostics only and are not treated as confirmatory p-values.

Top-k Sensitivity

The cumulative TRAD_T1 sums were inspected from k = 5 through k = 20.

Prime sums occur at:

• k = 5 → 337
• k = 8 → 1259
• k = 10 → 1327

The top-10 cutoff is therefore not the only nearby cutoff that produces a prime cumulative sum.

Prior Art

Abjad letter-number correspondence is historical and well documented. The Encyclopaedia Iranica entry on Abjad describes the use of Arabic letters as numerical values.

Token-frequency analysis of Quranic corpora is also established. The Quranic Arabic Corpus token-frequency example explicitly demonstrates listing the ten most frequent Quranic tokens under defined token representations.

A targeted search conducted on 2026-09-17 used combinations including:

• "1327" Quran Abjad "most frequent" words
• "1327" Quran Abjad
• "top 10" Quran word frequency Abjad

No source matching the exact formulation “the ten most frequent exact Quranic word forms have TRAD_T1 sum 1327” was identified in the sources examined.

This is an absence of an identified precedent in the searched sources, not proof that no earlier precedent exists.

Novelty remains under investigation.

Interpretation Standard

Fact

Under DATA-001 and the recovered TRAD_T1 convention:

• the exact RAW and BODY top-ten rankings contain the same ten forms;
• their TRAD_T1 values sum to 1327;
• 1327 is the 217th prime;
• the result survives the RAW/BODY corpus-view change;
• a defined orthographic normalization changes the sum to 1339, which is composite.

Statistical interpretation

Under the registered one-million-permutation challenge:

• RAW global-null prime rate: 11.7589%;
• RAW length-matched prime rate: 12.3992%;
• BODY results are similar.

The primality property is not statistically unusual under the tested null models.

Claim

QMR-008 establishes a reproducible arithmetic observation:

the ten most frequent exact word forms in DATA-001 sum to 1327 under the recovered literal TRAD_T1 Abjad convention.

Not claimed

QMR-008 does not establish:

• that 1327 is intrinsically or uniquely special;
• that top 10 is a statistically unique cutoff;
• statistical significance for the primality observation;
• robustness across every defensible Abjad normalization;
• established historical novelty;
• independent replication by an external researcher;
• supernatural origin;
• divine intent or theological significance.

No supernatural or divine conclusion follows from this result.

Why the Evidence Level Is E1

The deterministic pattern is well specified and reproducible under the frozen DATA-001 and TRAD_T1 rules.

However, E2 on Coran Codex denotes statistical support. The registered statistical challenge does not support treating primality as unusual: prime sums occur in approximately 12% of the tested null realizations.

The orthographic sensitivity also shows that primality depends on the recovered literal convention.

QMR-008 is therefore classified as E1 — Structured Pattern, not E2.

Limitations

The result depends on an explicitly recovered historical Abjad implementation in which characters outside the 28-letter table contribute zero.

The alternative orthographic sensitivity tested here is targeted, not exhaustive. Other defensible normalization conventions could be examined.

The statistical challenge tests two explicit null models, not every possible null model.

The top-10 rule is natural and historically present in the recovered record, but the study remains exploratory because the numerical result was first noticed before the modern statistical protocol was frozen.

The prior-art search cannot prove the absence of an earlier formulation.

Verdict

Status: Observation

Evidence level: E1

Classification: Exploratory

Novelty: Investigating

Discovery: No

The deterministic 1327 result is reproduced on DATA-001 in RAW and BODY under the recovered TRAD_T1 convention.

Its primality does not receive statistical support under the tested one-million-permutation null models, and the property does not survive the specified orthographic normalization.

QMR-008 is therefore retained as a reproducible structured observation with explicit negative statistical and robustness findings.

Reproducibility

Primary deterministic analysis:

analysis/qmr-008.mjs

Primary deterministic artifact:

artifacts/qmr-008/qmr-008-data001-report.json

Statistical challenge:

analysis/qmr-008-challenge.mjs

Statistical challenge artifact:

artifacts/qmr-008/qmr-008-challenge-report.json

Challenge parameters:

• permutations: 1,000,000
• base seed: 20260917
• k range: 5..20
• primary view: RAW
• sensitivity view: BODY
• primary Abjad: recovered literal TRAD_T1

QMR-008 was published after repository-level build, publication-route validation, and explicit publication authorization.