Pith Number

pith:W6JSEYBN

pith:2025:W6JSEYBNNVYH2Y6MOLI5SL3KYG

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Folkman's theorem and the primes

David J. Fern\'andez-Bret\'on

Folkman's theorem yields two new proofs that there are infinitely many prime numbers.

arxiv:2509.12025 v3 · 2025-09-15 · math.NT · math.CO

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\usepackage{pith}
\pithnumber{W6JSEYBNNVYH2Y6MOLI5SL3KYG}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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.

Claims

C1strongest claim

We provide two new proofs of the infinitude of prime numbers, using the additive Ramsey-theoretic result known as Folkman's theorem.

C2weakest assumption

Folkman's theorem (or Hindman's theorem) can be applied to suitably chosen colorings or subsets of the natural numbers in a way that directly forces the set of primes to be infinite.

C3one line summary

Two new proofs of the infinitude of primes are derived from Folkman's theorem.

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:05:33.381790Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b79322602d6d707d63cc72d1d92f6ac1bc49f191421aab44b2c8592bd0f1b707

Aliases

arxiv: 2509.12025 · arxiv_version: 2509.12025v3 · doi: 10.48550/arxiv.2509.12025 · pith_short_12: W6JSEYBNNVYH · pith_short_16: W6JSEYBNNVYH2Y6M · pith_short_8: W6JSEYBN

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/W6JSEYBNNVYH2Y6MOLI5SL3KYG \
  | 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: b79322602d6d707d63cc72d1d92f6ac1bc49f191421aab44b2c8592bd0f1b707

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3eb39d2e00213c76efa3e30c40d45793575788a61f039fe5799260ef49f61f38",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-09-15T15:05:56Z",
    "title_canon_sha256": "7bb4eb06c85bcfa5868c663ee95162dd582aa2185b33e94d2bb20a32cbcae7b1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.12025",
    "kind": "arxiv",
    "version": 3
  }
}