W-0055
A superpermutation on 12 symbols, found by Jakub Halfar. It beat the previous record, W-0053, by 81 letters, and was the record for n = 12 on Oct 5, 2026, when W-0056 was 7 letters shorter.
- Length
- 522,745,383
- Repeated occurrences
- 169,350
- Announced
- Oct 5, 2026
0123456789AB0123456789A0B123456789A01B23456789A012B3456789A0123B456789A01234B56789A012345B6789A0123456B789A01234567B89A0…
Windows
| 522,745,372 | windows of 12 consecutive letters | |
| = | 479,001,600 | distinct permutations, all 12! of them |
| + | 169,350 | repeated occurrences of a permutation |
| + | 43,574,422 | windows that are not permutations |
How it was found
Relocation with re-opening, then segment insertion (522,745,445 to 522,745,383 in 23 minutes).
Checking
Total check time: 8 s, including preparation but not time in the queue.
| Program | Source | Result | Time |
|---|---|---|---|
| classcheck | 41928cce | all 479,001,600 permutations appear, by rotation class | 3 s |
| bitmapcheck | 288b3f67 | agrees, by Lehmer rank | 2 s |
| wordhash | 94925fe4 | the SHA-256 of the word and of its mirror | 3 s |
Download
Download Detour (.detour) 44.9 kB, or 522.7 MB decoded
# check it yourself
detour decode W-0055.detour - | tr -d '\n' | shasum -a 256
tar xzf checkers-rs-source.tar.gz && cd checkers-rs && cargo build --release --locked
./target/release/classcheck 12 ../W-0055.detour 522745383
./target/release/bitmapcheck 12 ../W-0055.detour 522745383
./target/release/wordhash 12 ../W-0055.detour 522745383
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 = 12 and sync exponent 0. The file has 4,906,863 tokens: 1 START, 1 literal of 1 byte in all, and 4,906,861 deviations. Deviations by weight, from 1 to 12: 169,348 · 1,354,397 · 3,382,665 · 247 · 68 · 59 · 18 · 13 · 43 · 2 · 1 · 0.