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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 30.
Research chronicle 108 RECORDS
All Research Review Verification System
19:15:22 §1
SYSTEM Iteration 30 opened
19:15:24 §2
SYSTEM Iteration 30 started
19:15:24 §3
SYSTEM Initializing research run
19:15:24 §4
NOETHER NOETHER joined as Strategist
19:15:24 §5
SYSTEM Research started
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NOETHER Research planning started
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LITERATURE-01 Literature researcher
Reading the landscape around: Large-prime-factor construction via prime gaps
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,959
Cached input 0
Output tokens 503
Average latency 7.6 s
Failed calls 0
Cost (estimated) $0.000415
Joined 2026-09-25 19:15:44 UTC
Left 2026-09-25 19:18:54 UTC Recent activity 19:15:44 AGENT LITERATURE-01 joined as Literature Researcher 19:15:44 LITERATURE Literature search started 19:15:44 LITERATURE Literature search: 3 new of 3 19:15:44 LITERATURE Reviewed: An Upper Bound on the Divisor Counting Function 19:15:44 MEMORY Literature: An Upper Bound on the Divisor Counting Function 19:17:01 LITERATURE Literature search started 19:17:01 LITERATURE Indexed: A Prime Gap Counting Algorithm for Large and Small Prime Gaps 19:17:01 LITERATURE Indexed: Prime Clustering and Prime Gaps via the Pathak Continuum Compression Hypothesis (PCCH) Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
09 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration. 19:17:01
LITERATURE
Indexed: A Conjecture on Large Prime Gaps
19:17:01 LITERATURE Literature search: 3 new of 3
19:17:01 LITERATURE Reviewed: A Prime Gap Counting Algorithm for Large and Small Prime Gaps
19:17:01 MEMORY Literature: A Prime Gap Counting Algorithm for Large and Small Prime Gaps
19:18:54 AGENT LITERATURE-01 stood down Mission
Runtime 9 h 14 min
Iteration 57 of 57
Directions 331
Hypotheses 17
Experiments 266
Rejected paths 64 Current direction No direction is open.
Verified 0 Lean-verified intermediate lemmas A verified lemma covers exactly the declaration the kernel accepted. The problem stays open until it is settled either way. Literature
Indexed 109
Highly relevant 1 Iteration 30
Model calls 15
Estimated cost $0.009723 Budget remaining 99%
Iteration details & budget ↗
Research graph / proof lineage 9 objects · 3 links · 11 in complete graph
DIRECTION
DIRECTION Weighted divisor-count upper bound and greedy construction COMPLETED DIRECTION Probabilistic method and random subset density COMPLETED DIRECTION Divisor-chain layer decomposition and exact DP for small n COMPLETED DIRECTION Large-prime-factor construction via prime gaps COMPLETED DIRECTION Hypergraph independent set with fractional relaxation REJECTED DIRECTION Compression and density increment on the divisor poset REJECTED HYPOTHESIS
HYPOTHESIS H-001 REJECTED REVIEW
REVIEW Review (fail) FAIL PROOF
PROOF Large-prime-factor construction size computation v1 MARKDOWN Explore complete graph / 20 objects →