Erdos's Conjecture on Consecutive Integers Free of Certain Prime Factors
Let $n_k$ be the least $n > 2k$ such that $(n-k)(n-k+1)\cdots(n-1)$ has no prime factor in $(k, 2k)$. Erdos conjectured a superpolynomial lower bound; for all large $k$, $n_k > e^{\log^2 k / (20 \log\log k)}$.
Exact FrontierDelta
Scope and record
Occurred: Jun 18, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-discovered. Imported under CC BY 4.0.
Canonical aliases: Erdos's Conjecture on Consecutive Integers Free of Certain Prime Factors · Consecutive integers
Confidence: Not scored
Registry verification: unreviewed · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
Wouter van Doorn
human · human collaborator
Quanyu Tang
human · human collaborator
ChatGPT 5.5 Pro
model · ai model contributor · OpenAI / Harmonic
Aristotle
model · ai model contributor · OpenAI / Harmonic
Lineage and corrections
This event attributed to Wouter van Doorn
This event attributed to Quanyu Tang
This event attributed to ChatGPT 5.5 Pro
This event attributed to Aristotle