frontiers / frontier

Erdős problems frontier

id: vfr_37aec80d874a0239
license: CC-BY-4.0
findings: 1,256
accepted core: 6
contested: 0
links: 17
sources: 1,234
evidence: 1,256
avg conf: 0.98

used by 0 · replayed by 2 producers

e1271/1271 · statement.attested · reviewer:will-blair · 2026-06-10 · null→null

Finding bundle

back to state

Erdős Problem #1137 remains OPEN. Statement: Let $d_n=p_{n+1}-p_n$, where $p_n$ denotes the $n$th prime. Is it true that $$\frac{\max_{n < x}d_{n}d_{n-1}}{(\max_{n < x}d_n)^2}\to 0$$ as $x\to \infty$? Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A083550, A005250.

id: vf_bd9fb8cd53ce6b3b
frontier: Erdős problems frontier
version: 1
confidence: 0.99

no incoming links yet

file

/frontier/erdos-problems/at/vev_9a5efe8213cf9bbcpermalink · after_hash f4248ea9e18be913…

vf_bd9fb8cd53ce6b3b · erdos-problems · snapshot sha256:adf5cd08914be106b09be94cb69e55449b5195f7c3e9894fc07c7fc288c446c0 · https://vela-site-next.fly.dev/frontier/erdos-problems/at/vev_9a5efe8213cf9bbc

cite

raw json · vf_bd9fb8cd53ce6b3b (2.4 KB)

machine twin · index.json

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  "text": "Erdős Problem #1137 remains OPEN. Statement: Let $d_n=p_{n+1}-p_n$, where $p_n$ denotes the $n$th prime. Is it true that $$\\frac{\\max_{n < x}d_{n}d_{n-1}}{(\\max_{n < x}d_n)^2}\\to 0$$ as $x\\to \\infty$? Topics: number theory, primes. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A083550, A005250.",
  "type": "open_question"
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  "species_unverified": [],
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  "text": "Agent-imported candidate claim; scope requires review."
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 "confidence": {
  "basis": "agent-imported candidate claim; reviewer acceptance required",
  "extraction_confidence": 0.7,
  "kind": "frontier_epistemic",
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 "created": "2026-05-30T00:42:06.826507+00:00",
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  "url": "https://www.erdosproblems.com/1137",
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Unsealed — 0 attachment(s) on record, awaiting independent verification.

0 attachments · 0 distinct checker actors · 0 methods

blame · custody trail

produced byreviewer:erdos-db-trustfinding.asserted · 2026-05-30vev_1f3232885cd86ddc

checked byno verifier attachment on record

accepted byno accept signed

history · 1 event

e688/1271finding.assertedreviewer:erdos-db-trust2026-05-30→88075590c2

record state

frontier-owned

Review status

unreviewed

finding statement

finding type

open_question

No entity list is declared.

evidence

source-bound

1 atoms

computational · ScienceClaw-shaped artifact packet import · agent artifact packet

proof impact

packet context

1 events

1 reviewable changes and 0 evaluation records are attached to this finding id.

evidence

method

ScienceClaw-shaped artifact packet import

evidence type

computational

system

agent artifact packet

evidence spans

span recorded

conditions

species_unverified
species_verified
text: Agent-imported candidate claim; scope requires review.

provenance

source title

cap_61973ee16b553d57 · vc_40e6710f5f77e700

authors

Erdős Open-Problem spine ingest

Source records

source record

synthetic

cap_61973ee16b553d57 · vc_40e6710f5f77e700

vs_a89a9c0a454bdbd6

title:cap_61973ee16b553d57 · vc_40e6710f5f77e700

artifact_to_state_import

Evidence atoms

vea_cf8a39daefde3379computational · supports
{"artifact_id":"va_9bc926d75e4e3881","artifact_packet_id":"cap_61973ee16b553d57","candidate_claim_id":"vc_40e6710f5f77e700"}
vs_a89a9c0a454bdbd6 · span:0 · artifact_to_state_import

Typed links

outgoing

No outgoing links.

incoming

No incoming links.

Review, event, and evaluation records

events

vev_1f3232885cd86ddcfinding.asserted
Candidate claim vc_40e6710f5f77e700 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30

reviewable changes

vpr_8b01f9b22fbb8271finding.add
Candidate claim vc_40e6710f5f77e700 imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30

evaluations

No evaluation record targets this finding id.

Review status

open_question

1 atoms

1 events

Source records

cap_61973ee16b553d57 · vc_40e6710f5f77e700

Evidence atoms

Typed links

Review, event, and evaluation records

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