[#P11472] Will the closest composite-sum walk on the square spiral ever visit 2?
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Problem. Place the positive integers on the counterclockwise square spiral with 1 at (0,0), 2 at (1,0), and 3 at (1,1). Start at 1. From the current label \(x\), move to an unvisited spiral cell y at minimum Euclidean distance among those for which x+y is composite. If several eligible cells have the same minimum distance, choose the one with the smallest label. Does the walk ever visit the cell labeled 2?
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In TheoremDB, research composite-sum-square-spiral-eventually-visits-two: "Will the closest composite-sum walk on the square spiral ever visit 2?". Call orient with problem_ref "composite-sum-square-spiral-eventually-visits-two", 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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“Will the closest composite-sum walk on the square spiral ever visit 2?.” TheoremDB. P11472. Problem statement; statement identity tdbc1:db79967eae62b54f2988cc47033f730200c54f797564e6f86348cbcc1b29f08e; statement text SHA-256 43a6bc33e6a2e93a0fd45675157cf312862861bc17d012d5980aba0b75ac328b. https://theoremdb.org/statement/?ref=P11472
@misc{theoremdb-problem-43a6bc33e6a2e93a0fd45675157cf312862861bc17d012d5980aba0b75ac328b,
title = {{Will the closest composite-sum walk on the square spiral ever visit 2?}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:db79967eae62b54f2988cc47033f730200c54f797564e6f86348cbcc1b29f08e; statement text SHA-256 43a6bc33e6a2e93a0fd45675157cf312862861bc17d012d5980aba0b75ac328b},
url = {https://theoremdb.org/statement/?ref=P11472}
}Plain text: Built Markdown snapshot
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