Pith Number

pith:SXMCDNOL

pith:2025:SXMCDNOLZ3V6ID6AQPIDXEVKUD

not attested not anchored not stored refs pending

The strange story of an almost unknown prime number counter: The Rafael Barrett formula

Eduardo Mizraji

Rafael Barrett created a prime-counting formula in 1903 that stayed unknown until its 1935 publication.

arxiv:2509.19324 v7 · 2025-09-12 · math.HO

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SXMCDNOLZ3V6ID6AQPIDXEVKUD}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

Barrett's formula created in 1903 is a prime number counter that remained unknown for decades and poses a challenge worth analyzing after its 1935 publication.

C2weakest assumption

The historical facts about the formula's creation, discovery in the 1930s, and 1935 publication are accurate, and the formula is correctly presented without transcription errors.

C3one line summary

Presents Rafael Barrett's 1903 prime number counting formula and examines a challenge it could pose after its 1935 publication.

Receipt and verification

First computed	2026-06-12T01:09:14.022851Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

95d821b5cbceebe40fc083d03b92aaa0d25b247b5a87efdb636190f53eddd967

Aliases

arxiv: 2509.19324 · arxiv_version: 2509.19324v7 · doi: 10.48550/arxiv.2509.19324 · pith_short_12: SXMCDNOLZ3V6 · pith_short_16: SXMCDNOLZ3V6ID6A · pith_short_8: SXMCDNOL

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/SXMCDNOLZ3V6ID6AQPIDXEVKUD \
  | 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: 95d821b5cbceebe40fc083d03b92aaa0d25b247b5a87efdb636190f53eddd967

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d47273cbddc40152639afbacd47eff38d131cc69e533b2cd1270d8396d93413d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.HO",
    "submitted_at": "2025-09-12T22:58:48Z",
    "title_canon_sha256": "a56a7a38fbc67c8cf1c8b02a7badbb1f5a630b006751bb9c6c90edb760fca7c3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.19324",
    "kind": "arxiv",
    "version": 7
  }
}