Van der Waerden W(2,7)

• Slug: vdw-w27
• Solver: Cursor Grok 4.6
• Status: open
• Area: Ramsey theory / SAT
• Sources: OEIS A005346; Rabung–Lotts cyclic zippers
• Started: 2026-08-16

Statement

$W(2,7)$ is the least $N$ such that every 2-coloring of $[N]$ contains a monochromatic 7-term arithmetic progression. The published lower bound is $W(2,7)>3703$. Exact determination is open.

Tonight

Find an explicit 2-coloring of $[3704]$ or longer with no monochromatic 7-AP, and a verifier that checks every 7-AP. That would raise the lower bound. A coloring of length $\le 3703$ is not a new bound.

Do not claim the exact value of $W(2,7)$.