Pith Number

pith:W3QIRNS3

pith:2012:W3QIRNS3TBOHHRFNBHJN3MZYF6

not attested not anchored not stored refs pending

The n-th prime asymptotically

Juan Arias de Reyna, Toulisse Jeremy

arxiv:1203.5413 v2 · 2012-03-24 · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W3QIRNS3TBOHHRFNBHJN3MZYF6}

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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.

Cited by

1 paper in Pith

The n-th prime exponentially

Receipt and verification

First computed	2026-05-18T02:55:50.076334Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b6e088b65b985c73c4ad09d2ddb3382f8120ed73e50df460442ecd6cf2eb3329

Aliases

arxiv: 1203.5413 · arxiv_version: 1203.5413v2 · doi: 10.48550/arxiv.1203.5413 · pith_short_12: W3QIRNS3TBOH · pith_short_16: W3QIRNS3TBOHHRFN · pith_short_8: W3QIRNS3

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/W3QIRNS3TBOHHRFNBHJN3MZYF6 \
  | 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: b6e088b65b985c73c4ad09d2ddb3382f8120ed73e50df460442ecd6cf2eb3329

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a6c543c37a6e751bdf5e6e079bc27b432cb1d721d4c0909c9ae7cc48337b15d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-03-24T13:43:19Z",
    "title_canon_sha256": "ad5a648e58604b7a986368a2b23093b3602f0f705278c5a42ce014c0246ef3e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.5413",
    "kind": "arxiv",
    "version": 2
  }
}