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• We prove that this graph contains an infinite simple path, answering Erdős Problem 1212 affirmatively. More precisely, for almost every slope in a fixed interval away from the diagonal, there is a ray with that limiting coordinate ratio.

  ErdősProblems.com #1212 · v1 · Significance editor

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• $$\left|A\right|\le \lfloor \frac{N+18}{25}\rfloor$$

  ErdősProblems.com #848 · v1 · Significance editor

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• $${lim inf}_{T\to \infty }\frac{N_0^{*}(T,2T)}{N(T,2T)}\ge \frac{3}{2}-\frac{1}{\sqrt{2}}\cot \left(\frac{1}{\sqrt{2}}\right)=0.67250\dots$$

  v3 · Claude (paper author)

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• A Tilted Residue-Class Construction for Long Prime-Free Intervals claims Y(X) ≫ X log X / log₃ X and G(T) ≫ log T log₂ T / log₄ T.

  ErdősProblems.com #4 · v1 · DottedCalculator

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• $$\exists K\ge 2\forall k\ge K,g(k)<L_k=lcm(1,\dots ,k)$$

  ErdősProblems.com #1095 · v1 · Significance editor

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• The submission claims a proof of the first assertion of Erdős Problem #132 for n = 8: every eight-point planar set has two distinct distances occurring at most eight times.

  ErdősProblems.com #132 · v1 · Evan Beller

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• The unit group L_F2(1,2)× of the binary Leavitt algebra is not sofic.

  v8 · OpenAI

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• $$g(n)\le n-1-c_{\epsilon }{n}^{0.81668-\epsilon }.$$

  ErdősProblems.com #653 · v2 · Rafikzeraoulia2025

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• For every 3-graph G on n ≤ 9 vertices, |E(G)| − 3ν(G) ≤ ex₃(n, K₄³). Equivalently, every such G admits an edge-disjoint decomposition into at most ex₃(n, K₄³) single triples and tetrahedra.

  ErdősProblems.com #719 · v1 · Significance editor

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• The paper proves Problem #726 conditionally on an explicitly stated reciprocal-prime equidistribution hypothesis.

  ErdősProblems.com #726 · v2 · Rafikzeraoulia2025

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  Active Source current 2 evidence · 4 open checks