Pith Number

pith:RELKGPIG

pith:2016:RELKGPIGNK3ODLA5SLSZWQZ5IY

not attested not anchored not stored refs pending

New bounds for the sum of the first $n$ prime numbers

Christian Axler

arxiv:1606.06874 v2 · 2016-06-22 · 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{RELKGPIGNK3ODLA5SLSZWQZ5IY}

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

The Landau function and the Riemann Hypothesis

Receipt and verification

First computed	2026-05-17T23:50:01.728242Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8916a33d066ab6e1ac1d92e59b433d461321d1245ca8ad3c878d78814c2d83fa

Aliases

arxiv: 1606.06874 · arxiv_version: 1606.06874v2 · doi: 10.48550/arxiv.1606.06874 · pith_short_12: RELKGPIGNK3O · pith_short_16: RELKGPIGNK3ODLA5 · pith_short_8: RELKGPIG

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/RELKGPIGNK3ODLA5SLSZWQZ5IY \
  | 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: 8916a33d066ab6e1ac1d92e59b433d461321d1245ca8ad3c878d78814c2d83fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "258b804421facd27dd637bea7da18b8b9634d6fa409f30876ab4116b9ce7c66d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-06-22T10:06:14Z",
    "title_canon_sha256": "c3c0924c82b677f9046565487fdb3ff2f6a9a98e5cd2a7dbdb7fdbd2add35480"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.06874",
    "kind": "arxiv",
    "version": 2
  }
}