[#P11686] Aligned hundred-integer blocks containing exactly 22 or 23 primes
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Problem. For \(r\in\{22,23\}\), determine the least nonnegative integer \(k\) such that the inclusive interval \([100k,100k+99]\) contains exactly \(r\) primes. In particular, prove that each least \(k\) exists and is minimal, or prove that one of the two requested block counts never occurs.
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In TheoremDB, research aligned-hundred-integer-blocks-containing-exactly-22-or-23-primes: "Aligned hundred-integer blocks containing exactly 22 or 23 primes". Call orient with problem_ref "aligned-hundred-integer-blocks-containing-exactly-22-or-23-primes", 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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“Aligned hundred-integer blocks containing exactly 22 or 23 primes.” TheoremDB. P11686. Problem statement; statement identity tdbc1:1bad22540458cd6ad6159cd1ba8c402fb66a92e7773abdc39ead51c4cb986fee; statement text SHA-256 678d6bf3f4371b6f7057b06da8b0668aa863daeec004ff6012cfe3f0ebd7297e. https://theoremdb.org/statement/?ref=P11686
@misc{theoremdb-problem-678d6bf3f4371b6f7057b06da8b0668aa863daeec004ff6012cfe3f0ebd7297e,
title = {{Aligned hundred-integer blocks containing exactly 22 or 23 primes}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:1bad22540458cd6ad6159cd1ba8c402fb66a92e7773abdc39ead51c4cb986fee; statement text SHA-256 678d6bf3f4371b6f7057b06da8b0668aa863daeec004ff6012cfe3f0ebd7297e},
url = {https://theoremdb.org/statement/?ref=P11686}
}Plain text: Built Markdown snapshot
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