Pith Number

pith:TXJ2J6JP

pith:2021:TXJ2J6JPDR6QESGWBTU3SMP6TT

not attested not anchored not stored refs pending

Explicit Interval Estimates for Prime Numbers

Ethan S. Lee, Michaela Cully-Hugill

arxiv:2103.05986 v3 · 2021-03-10 · 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{TXJ2J6JPDR6QESGWBTU3SMP6TT}

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

Effective short intervals containing primes

Receipt and verification

First computed	2026-07-05T04:57:22.414129Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9dd3a4f92f1c7d0248d60ce9b931fe9cc3c73b7265970f7c3d827616e3d9ae5e

Aliases

arxiv: 2103.05986 · arxiv_version: 2103.05986v3 · doi: 10.48550/arxiv.2103.05986 · pith_short_12: TXJ2J6JPDR6Q · pith_short_16: TXJ2J6JPDR6QESGW · pith_short_8: TXJ2J6JP

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/TXJ2J6JPDR6QESGWBTU3SMP6TT \
  | 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: 9dd3a4f92f1c7d0248d60ce9b931fe9cc3c73b7265970f7c3d827616e3d9ae5e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c28eba9b5f4e1b186503f3b19f648508322d80ce59a8e1ffc183424349d4f27",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2021-03-10T10:49:22Z",
    "title_canon_sha256": "42eba4d7dcb5bd20689075a1b9159a34ec835cf42a8e87013513ab7e1bb5890a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2103.05986",
    "kind": "arxiv",
    "version": 3
  }
}