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

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cap_61973ee16b553d57 · vc_16b24d9378401eb5

id: vs_f2f2c224d207656c
frontier: Erdős problems frontier
type: synthetic_report

source boundary

frontier-owned

synthetic

finding bindings

record context

1 findings

evidence atoms

materialized

1 atoms

review context

inspectable

1 events

4 reviewable changes and 0 evaluations are attached through this source or its findings.

citation

external source

locator

title:cap_61973ee16b553d57 · vc_16b24d9378401eb5

imported

2026-05-30T00:42:06.826507+00:00

extraction mode

artifact_to_state_import

authors

Erdős Open-Problem spine ingest

caveats

source requires human review before being treated as evidence

Bound findings

Erdős Problem #203 remains OPEN. Statement: Is there an integer $m$ with $(m, 6) = 1$ such that none of $2^k \cdot 3^\ell \cdot m + 1$ are prime, for any $k, \ell \ge 0$? Topics: primes, covering systems. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.
open_question · vf_7a226f29da63b3f3

Evidence atoms

vea_c47de0ca62bb0e1bcomputational · supports
{"artifact_id":"va_9bc926d75e4e3881","artifact_packet_id":"cap_61973ee16b553d57","candidate_claim_id":"vc_16b24d9378401eb5"}

Review, event, and evaluation records

events

vev_7dd3b83b53d0c3ddfinding.asserted
Candidate claim vc_16b24d9378401eb5 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30

reviewable changes

vpr_34c8e23ed1e7778bfinding.note
SEMANTIC-EDGE DRAFT -> Erdos #279 (vf_a8fab4b7d1d7cb28) [shares_technique, confidence 0.65]: Both rely on choosing congruence classes a_p mod p (covering congruences) to force every relevant integer into a prescribed residue, the shared covering-system method. -- LLM-drafted (20-agent extraction, 2026-06); NOT adjudicated. Accept or reject via `vela proposals accept/reject` under reviewer authority.
pending_review · agent:semantic-edge-extractor · 2026-06-10
vpr_540ada549eaa142efinding.note
SEMANTIC-EDGE DRAFT -> Erdos #1113 (vf_6ea4019ad9017c9b) [shares_technique, confidence 0.8]: 203 asks for m making 2^k·3^l·m+1 never prime; 1113's covering-set framework for k·2^n+1 (Sierpiński numbers) is the same prime-blocking-by-covering construction extended to two exponents. -- LLM-drafted (20-agent extraction, 2026-06); NOT adjudicated. Accept or reject via `vela proposals accept/reject` under reviewer authority.
pending_review · agent:semantic-edge-extractor · 2026-06-10
vpr_8751cf625edd9abdfinding.note
SEMANTIC-EDGE DRAFT -> Erdos #7 (vf_6e126f3f5046840d) [shares_technique, confidence 0.75]: Both are resolved by constructing covering systems of congruences; 203 needs a covering of the exponents (k,l) of 2^k·3^l·m+1, exactly the covering-system machinery that 7 studies in the odd-modulus case. -- LLM-drafted (20-agent extraction, 2026-06); NOT adjudicated. Accept or reject via `vela proposals accept/reject` under reviewer authority.
pending_review · agent:semantic-edge-extractor · 2026-06-10
vpr_943918e21ad152acfinding.add
Candidate claim vc_16b24d9378401eb5 imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30

evaluations

No evaluation rows are attached.