W-0065
A superpermutation on 13 symbols, found by Jakub Halfar. It beat the previous record, W-0061, by 114,042 letters, and was the record for n = 13 on Oct 6, 2026, when W-0067 was 313 letters shorter.
- Length
- 6,747,802,875
- Repeated occurrences
- 1,798,297
- Announced
- Oct 6, 2026
0123456789ABC0123456789AB0C123456789AB01C23456789AB012C3456789AB0123C456789AB01234C56789AB012345C6789AB0123456C789AB0123…
Windows
| 6,747,802,863 | windows of 13 consecutive letters | |
| = | 6,227,020,800 | distinct permutations, all 13! of them |
| + | 1,798,297 | repeated occurrences of a permutation |
| + | 518,983,766 | windows that are not permutations |
How it was found
Pantone's construction on a new selection: 23,808 closed trails instead of 252,000.
Checking
Total check time: 2 min 7 s, including preparation but not time in the queue.
| Program | Source | Result | Time |
|---|---|---|---|
| classcheck | 41928cce | all 6,227,020,800 permutations appear, by rotation class | 46 s |
| bitmapcheck | 288b3f67 | agrees, by Lehmer rank | 40 s |
| wordhash | 94925fe4 | the SHA-256 of the word and of its mirror | 41 s |
Download
Download Detour (.detour) 402.7 kB, or 6.7 GB decoded
# check it yourself
detour decode W-0065.detour - | tr -d '\n' | shasum -a 256
tar xzf checkers-rs-source.tar.gz && cd checkers-rs && cargo build --release --locked
./target/release/classcheck 13 ../W-0065.detour 6747802875
./target/release/bitmapcheck 13 ../W-0065.detour 6747802875
./target/release/wordhash 13 ../W-0065.detour 6747802875
Decoding needs detour; see the Detour format for how to build and install it. The checkers are in checkers-rs-source.tar.gz, which needs Rust 1.89 or later; each one decodes the file itself, so the word is never written out.
The file's header gives n = 13 and sync exponent 0. The file has 57,704,733 tokens: 1 START, 1 literal of 1 byte in all, and 57,704,731 deviations. Deviations by weight, from 1 to 13: 1,798,297 · 16,143,368 · 39,755,590 · 2,250 · 699 · 1,187 · 435 · 1,324 · 528 · 723 · 121 · 204 · 5.