Pith Number

pith:WA5Z64LO

pith:2013:WA5Z64LOHYTQQOARH3RK6OUYPV

not attested not anchored not stored refs pending

Conjecture on the value of Pi(10^26), the number of primes less than 10^26

Vladimir Pletser

arxiv:1307.4444 v1 · 2013-07-16 · 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{WA5Z64LOHYTQQOARH3RK6OUYPV}

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	2026-05-18T03:18:17.952776Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b03b9f716e3e270838113ee2af3a987d7b64579a15e6ef5bef0070658da7a39d

Aliases

arxiv: 1307.4444 · arxiv_version: 1307.4444v1 · doi: 10.48550/arxiv.1307.4444 · pith_short_12: WA5Z64LOHYTQ · pith_short_16: WA5Z64LOHYTQQOAR · pith_short_8: WA5Z64LO

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/WA5Z64LOHYTQQOARH3RK6OUYPV \
  | 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: b03b9f716e3e270838113ee2af3a987d7b64579a15e6ef5bef0070658da7a39d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c851b0364334bc031e7e0d7e773bed7a4705bf1e13bdac9cdae6c773e519097",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-07-16T22:53:28Z",
    "title_canon_sha256": "06c43d71090707525779485f29f89f9a0c33869c2f27e957f83ae69aa0aab182"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.4444",
    "kind": "arxiv",
    "version": 1
  }
}