Pith Number

pith:TPSDUYI5

pith:2006:TPSDUYI5IMIF72ZOF63ZZE6Y7Z

not attested not anchored not stored refs pending

Small gaps between products of two primes

C.Y. Yildirim, D. A. Goldston, J. Pintz, S.W. Graham

arxiv:math/0609615 v1 · 2006-09-21 · 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{TPSDUYI5IMIF72ZOF63ZZE6Y7Z}

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.

Receipt and verification

First computed	2026-05-18T02:57:45.502989Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9be43a611d43105feb2e2fb79c93d8fe7ec3f0cada3a55617a27464ad21e5406

Aliases

arxiv: math/0609615 · arxiv_version: math/0609615v1 · doi: 10.48550/arxiv.math/0609615 · pith_short_12: TPSDUYI5IMIF · pith_short_16: TPSDUYI5IMIF72ZO · pith_short_8: TPSDUYI5

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/TPSDUYI5IMIF72ZOF63ZZE6Y7Z \
  | 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: 9be43a611d43105feb2e2fb79c93d8fe7ec3f0cada3a55617a27464ad21e5406

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a5c93f1513ac0447954ca1a82c6a93ebef100976787c5496979ba2ca2cf773e9",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2006-09-21T19:05:55Z",
    "title_canon_sha256": "00dba92015fdd4a618aaeec083e37ff1d827869b3974922363cd74944d9ef52f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0609615",
    "kind": "arxiv",
    "version": 1
  }
}