- Proved at least
- 6,746,626,957
- Shortest known
- 6,747,802,319
- Gap
- 1,175,362
The record is W-0075, found by Jakub Halfar on Oct 20, 2026.
The bounds over time
Every verified word
| Word | Length | Found by | Date | Shorter than the record before | Repeats | Other windows |
|---|---|---|---|---|---|---|
| W-0075 | 6,747,802,319 | Jakub Halfar | Oct 20, 2026 | 74 | 1,797,743 | 518,983,764 |
| W-0068 | 6,747,802,393 | Jakub Halfar | Oct 8, 2026 | 169 | 1,797,600 | 518,983,981 |
| W-0067 | 6,747,802,562 | Jakub Halfar | Oct 6, 2026 | 313 | 1,798,294 | 518,983,456 |
| W-0065 | 6,747,802,875 | Jakub Halfar | Oct 6, 2026 | 114,042 | 1,798,297 | 518,983,766 |
| W-0061 | 6,747,916,917 | Jakub Halfar | Oct 5, 2026 | 504 | 1,693,443 | 519,202,662 |
| W-0059 | 6,747,917,421 | Jakub Halfar | Oct 5, 2026 | 43 | 1,693,434 | 519,203,175 |
| W-0057 | 6,747,917,464 | Jakub Halfar | Oct 5, 2026 | 34 | 1,693,435 | 519,203,217 |
| W-0054 | 6,747,917,498 | Jakub Halfar | Oct 5, 2026 | 472 | 1,693,434 | 519,203,252 |
| W-0050 | 6,747,917,970 | Jakub Halfar | Oct 4, 2026 | 88 | 1,693,436 | 519,203,722 |
| W-0043 | 6,747,918,058 | Jakub Halfar | Oct 3, 2026 | 8 | 1,693,436 | 519,203,810 |
| W-0036 | 6,747,918,066 | Jay Pantone  jaypantone |
Oct 1, 2026 | 49,732 | 1,693,436 | 519,203,818 |
| W-0031 | 6,747,967,798 | Jay Pantone jaypantone |
Sep 29, 2026 | 19,328 | 1,693,440 | 519,253,546 |
| W-0027 | 6,747,987,126 | Jay Pantone jaypantone |
Sep 29, 2026 | 1,580,883 | 1,693,440 | 519,272,874 |
| W-0020 | 6,749,568,009 | Uku Raudvere | Jul 27, 2026 | — | 0 | 522,547,197 |
Bounds at n = 13
| Upper bounds | ||
| 6,749,568,010 | Egan's bound, Greg Egan, 2018 | Paper |
| 6,749,568,009 | Egan's bound minus one, Uku Raudvere, 2026 | Lean, kernel-checked |
| 6,748,993,440 | The 101/120 bound, Jay Pantone jaypantone, 2026 | Lean, kernel-checked |
| 6,748,116,480 | The 3/5 bound, Jay Pantone jaypantone, 2026 | Lean, kernel-checked |
| 6,747,802,319 | W-0075, the shortest known word, Jakub Halfar, 2026 | Checked word |
| 1,175,362 | gap | |
| Lower bounds | ||
| 6,746,626,957 | S(13) ≥ 6,746,626,957, Jakub Halfar, 2026 | Lean, kernel-checked |
| 6,746,626,531 | Pantone's bound, Jay Pantone jaypantone, 2026 | Lean, statement reviewed |
| 6,746,615,766 | Halfar's general bound, Jakub Halfar, 2026 | Lean, statement reviewed |
| 6,746,553,315 | Kisic's bound, Marin Kisic and Jakub Halfar, 2026 | Lean, kernel-checked |
| 6,746,523,219 | Liu's bound, Xiaolong Liu, 2026 | Lean, statement reviewed |
| 6,746,243,919 | The Hunter–Raudvere bound, Zach Hunter and Uku Raudvere, 2026 | Lean, statement reviewed |
| 6,746,084,362 | Raudvere's bound, Uku Raudvere, 2026 | Lean, kernel-checked |
| 6,745,939,211 | 4chan + 1, Robin Houston, 2018 | Lean proof |
| 6,745,939,210 | The 4chan bound, Anonymous 4chan poster, Robin Houston, Jay Pantone jaypantone and Vince Vatter, 2011 | Paper |