Superpermutation Almanac

n = 9

‹ n = 8n = 10 ›
Proved at least
408,469
Shortest known
408,731
Gap
262

The record is W-0038, found by rumstd on Oct 2, 2026.

The bounds over time

Every verified word

WordLengthFound byDateShorter than the record beforeRepeatsOther windows
W-0038 408,731 rumstd Oct 2, 2026 1 336 45,507
W-0037 408,732 Jay Pantone jaypantone Oct 1, 2026 4 336 45,508
W-0029 408,736 Jay Pantone jaypantone Sep 29, 2026 229 336 45,512
W-0017 408,965 William Echols Jul 26, 2026 1 0 46,077
W-0012 408,966 Greg Egan Oct 20, 2018 — 0 46,078

Bounds at n = 9

Upper bounds
408,966Egan's bound, Greg Egan, 2018Paper
408,965Egan's bound minus one, Uku Raudvere, 2026Lean, kernel-checked
408,846The 101/120 bound, Jay Pantone jaypantone, 2026Lean, kernel-checked
408,731W-0038, the shortest known word, rumstd, 2026Checked word
262gap
Lower bounds
408,469S(9) ≥ 408,469, Jakub Halfar, 2026Lean, kernel-checked
408,469Pantone's bound, Jay Pantone jaypantone, 2026Lean, statement reviewed
408,465Halfar's general bound, Jakub Halfar, 2026Lean, statement reviewed
408,433Kisic's bound, Marin Kisic and Jakub Halfar, 2026Lean, kernel-checked
408,418Liu's bound, Xiaolong Liu, 2026Lean, statement reviewed
408,338The Hunter–Raudvere bound, Zach Hunter and Uku Raudvere, 2026Lean, statement reviewed
408,289Raudvere's bound, Uku Raudvere, 2026Lean, kernel-checked
408,2474chan + 1, Robin Houston, 2018Lean proof
408,246The 4chan bound, Anonymous 4chan poster, Robin Houston, Jay Pantone jaypantone and Vince Vatter, 2011Paper

All bounds, with their formulas