Pith Number

pith:C3YF3QZS

pith:2008:C3YF3QZSMIFY2GIXH4MMD6R6YJ

not attested not anchored not stored refs pending

There are infinitely many prime numbers in all arithmetic progressions with first term and difference coprime

Peter Gustav Lejeune Dirichlet

arxiv:0808.1408 v2 · 2008-08-10 · math.HO · 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{C3YF3QZSMIFY2GIXH4MMD6R6YJ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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

A Hilbert-Kunz function with a periodic term that has a given period

Receipt and verification

First computed	2026-05-18T02:32:55.427829Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

16f05dc332620b8d19173f18c1fa3ec24c910259820ef4872d4d3e7caa8d7c93

Aliases

arxiv: 0808.1408 · arxiv_version: 0808.1408v2 · doi: 10.48550/arxiv.0808.1408 · pith_short_12: C3YF3QZSMIFY · pith_short_16: C3YF3QZSMIFY2GIX · pith_short_8: C3YF3QZS

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/C3YF3QZSMIFY2GIXH4MMD6R6YJ \
  | 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: 16f05dc332620b8d19173f18c1fa3ec24c910259820ef4872d4d3e7caa8d7c93

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05d4797a843fb2669f0bc99e810348059beb341c5e108e6645bf1c1d7a3fc6a0",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/publicdomain/",
    "primary_cat": "math.HO",
    "submitted_at": "2008-08-10T14:57:30Z",
    "title_canon_sha256": "3bb8817c3d9302fca8034064da20b381723eb898c74bd16df4173466e2eec149"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0808.1408",
    "kind": "arxiv",
    "version": 2
  }
}