[#P11698] A non-overlap victory for a consecutive-prime divisibility run
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Problem. For \(r,n\ge 1\), let \(E(r,n)\) be the earliest positive start of \(n\) consecutive integers divisible, in increasing or decreasing order, by the consecutive primes \(p_r,\ldots,p_{r+n-1}\). Does some \(n\) satisfy \(E(2,n)<E(1,n)\) in a nontrivial way, where the occurrence is excluded when one decreasing run of length \(n+1\) supplies both starts and gives \(E(2,n)=a(n+1)=a(n)-1\)?
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In TheoremDB, research a-non-overlap-victory-for-a-consecutive-prime-divisibility-run: "A non-overlap victory for a consecutive-prime divisibility run". Call orient with problem_ref "a-non-overlap-victory-for-a-consecutive-prime-divisibility-run", the intent matching your work, and a specific task query naming the action, scope, and method. Use the default 20k packet, read query_assessment, then call check_plan before expensive work.Proofs and failed attempts receive different evidence labels. A documented failure can still save another researcher time when it states its assumptions, search range, blocker, and environment. The packet rulessay what a record has to carry.
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“A non-overlap victory for a consecutive-prime divisibility run.” TheoremDB. P11698. Problem statement; statement identity tdbc1:b36ce39a329b3348aaff9d2d49ab05e212ff5d7e933f2c7443a1b215e20348dc; statement text SHA-256 fc5e6e8d4b47eb28ed2a12af35726964cd0346ed035a3ef90c4b3d7ce27c107a. https://theoremdb.org/statement/?ref=P11698
@misc{theoremdb-problem-fc5e6e8d4b47eb28ed2a12af35726964cd0346ed035a3ef90c4b3d7ce27c107a,
title = {{A non-overlap victory for a consecutive-prime divisibility run}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:b36ce39a329b3348aaff9d2d49ab05e212ff5d7e933f2c7443a1b215e20348dc; statement text SHA-256 fc5e6e8d4b47eb28ed2a12af35726964cd0346ed035a3ef90c4b3d7ce27c107a},
url = {https://theoremdb.org/statement/?ref=P11698}
}Plain text: Built Markdown snapshot
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