Pith Number

pith:R3BHCVNW

pith:2026:R3BHCVNWFFSJWR4IOSMXLAOEL4

not attested not anchored not stored refs pending

Frequency Ordered Ratio Families Arising from the Factorization of $p_{m-1}+1$

Alexander R Povolotsky

Frequencies of ratios from factoring p_{m-1}+1 for m in A223881 follow an asymptotic ordering predicted by primes in arithmetic progressions.

arxiv:2605.08256 v2 · 2026-05-07 · math.NT

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\pithnumber{R3BHCVNWFFSJWR4IOSMXLAOEL4}

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Record completeness

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4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We propose a heuristic asymptotic model explaining the observed frequency ordering via classical results on primes in arithmetic progressions and support the model with numerical log-log analysis.

C2weakest assumption

That the observed frequencies of the ratio families R_m are asymptotically governed by the distribution of primes in arithmetic progressions in a manner that can be captured by a heuristic model without post-hoc parameter tuning to the specific data set.

C3one line summary

Frequency-ordering the smaller factors R_m in p_{m-1}+1 factorizations for m where the largest factor exceeds m produces a new sequence explained by a heuristic model using the distribution of primes in arithmetic progressions.

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-28T01:04:08.636144Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8ec27155b629649b478874997581c45f3e69ca3bd4c4a3f1c60efbd7d371b817

Aliases

arxiv: 2605.08256 · arxiv_version: 2605.08256v2 · doi: 10.48550/arxiv.2605.08256 · pith_short_12: R3BHCVNWFFSJ · pith_short_16: R3BHCVNWFFSJWR4I · pith_short_8: R3BHCVNW

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/R3BHCVNWFFSJWR4IOSMXLAOEL4 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 8ec27155b629649b478874997581c45f3e69ca3bd4c4a3f1c60efbd7d371b817

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "641880a4a7dd8741e8a3951676a245f339c9ea9d1ab3e24989a943161ea71d9f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-05-07T20:41:46Z",
    "title_canon_sha256": "c6ac11d844b403c2e10ecb1c2261c9101da73c842e76f43e73bcba80bea0fb23"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.08256",
    "kind": "arxiv",
    "version": 2
  }
}