Pith Number

pith:OMRRRHJ7

pith:2019:OMRRRHJ72UWJGKDYIO4OBFBD73

not attested not anchored not stored refs pending

Verifying the Firoozbakht, Nicholson, and Farhadian conjectures up to the 81st maximal prime gap

Matt Visser (Victoria University of Wellington)

arxiv:1904.00499 v2 · 2019-03-31 · 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{OMRRRHJ72UWJGKDYIO4OBFBD73}

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

Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$

Receipt and verification

First computed	2026-07-05T10:54:28.298990Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7323189d3fd52c93287843b8e09423feebd4f6fd569f12f59efb668c129ea761

Aliases

arxiv: 1904.00499 · arxiv_version: 1904.00499v2 · doi: 10.48550/arxiv.1904.00499 · pith_short_12: OMRRRHJ72UWJ · pith_short_16: OMRRRHJ72UWJGKDY · pith_short_8: OMRRRHJ7

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/OMRRRHJ72UWJGKDYIO4OBFBD73 \
  | 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: 7323189d3fd52c93287843b8e09423feebd4f6fd569f12f59efb668c129ea761

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab147cb41692ea39eb5a19d86ae0b75ab1c77534a8bbc9b47f71ce82ef677416",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-03-31T22:33:31Z",
    "title_canon_sha256": "201b2083921bec70acc98f96aad0d3b051d189508328b6a5ebd2a3e7282528b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.00499",
    "kind": "arxiv",
    "version": 2
  }
}