Will the closest composite-sum walk on the square spiral ever visit 2?
TheoremDB P11472 · number theory
Inferred from the community field; finer classification has not been reviewed.
Problem statement
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 , 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?
Lean 4
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Background
Additional formulation recorded by the source
x_1=1,\quad x_{n+1}=\min_{\text{label}}\operatorname*{argmin}_{y\notin{x_1,\ldots,x_n},\ x_n+y\ \mathrm{composite}}|c(y)-c(x_n)|_2;\qquad \exists n,\ x_n=2,?
Progress & source assessment
Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution.
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Recorded progress
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Discussion
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