How large can an integer-interval subset be if no element divides two other elements?
BLOCKED
2 h 33 min
Determine how large a subset of an integer interval can be when no element of the subset divides two other elements of it. Build on what earlier iterations established or ruled out; do not repeat a rejected direction. Push the best upper and lower bounds you can justify, and formalise in Lean any lemma you actually prove.
Number theoryIteration 7 of 7Started 2026-09-25 11:13:58 UTC
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Checking prior art and known barriers for: Primitive‑Set Extension via Prime‑Factor Constraints Large‑prime‑factor construction yields near‑full density
Model
Model used
together / openai/gpt-oss-120b
Routing profile
cheap_reasoning
Usage
Model calls
2
Input tokens
1,990
Cached input
138
Output tokens
939
Average latency
3.8 s
Failed calls
0
Cost (estimated)
$0.000862
Joined
2026-09-25 11:36:54 UTC
Left
2026-09-25 11:41:48 UTC
Recent activity
AGENTLITERATURE-02 joined as Literature Researcher
LITERATURELiterature search started
LITERATUREIndexed: Two Lower Estimates in Greedy Approximation
LITERATUREIndexed: Two Lower Estimates in Greedy Approximation
LITERATUREIndexed: A Greedy Search Based Method with Optimized Lower Bound for QC-LDPC Codes
LITERATURELiterature search: 3 new of 3
LITERATUREReviewed: Two Lower Estimates in Greedy Approximation
MEMORYLiterature: Two Lower Estimates in Greedy Approximation
Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
LITERATURE
Literature search started
LITERATUREIndexed: Numbers in a given set with (or without) a large prime factor
LITERATUREIndexed: Determining the Next Prime Using the Least Prime Factor Method
LITERATUREIndexed: On the quotient between the greatest prime factor and the least prime factor
LITERATURELiterature search: 3 new of 3
LITERATUREReviewed: Numbers in a given set with (or without) a large prime factor
MEMORYLiterature: Numbers in a given set with (or without) a large prime factor