W-0075
A superpermutation on 13 symbols, found by Jakub Halfar. It beat the previous record, W-0068, by 74 letters, and is the record for n = 13.
- Length
- 6,747,802,319
- Repeated occurrences
- 1,797,743
- Announced
- Oct 20, 2026
0123456789ABC0123456789AB0C123456789AB01C23456789AB012C3456789AB0123C456789AB01234C56789AB012345C6789AB0123456C789AB0123…
Windows
| 6,747,802,307 | windows of 13 consecutive letters | |
| = | 6,227,020,800 | distinct permutations, all 13! of them |
| + | 1,797,743 | repeated occurrences of a permutation |
| + | 518,983,764 | windows that are not permutations |
How it was found
The same two moves as Halfar's 522,736,969 (Echols's re-opening of consecutive trails, Theo H.'s phase move) with his local search, on selection N; 74 below his 6,747,802,393 and 115,747 below Pantone's 6,747,918,066.
Checking
Total check time: 1 min 50 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 | 41 s |
| bitmapcheck | 288b3f67 | agrees, by Lehmer rank | 33 s |
| wordhash | 94925fe4 | the SHA-256 of the word and of its mirror | 35 s |
Download
Download Detour (.detour) 398.6 kB, or 6.7 GB decoded
# check it yourself
detour decode W-0075.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-0075.detour 6747802319
./target/release/bitmapcheck 13 ../W-0075.detour 6747802319
./target/release/wordhash 13 ../W-0075.detour 6747802319
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 57,700,629 tokens: 1 START, 1 literal of 1 byte in all, and 57,700,627 deviations. Deviations by weight, from 1 to 13: 1,797,743 · 16,138,439 · 39,757,120 · 1,535 · 1,257 · 1,240 · 445 · 1,404 · 527 · 710 · 84 · 118 · 5.