W-0054
A superpermutation on 13 symbols, found by Jakub Halfar. It beat the previous record, W-0050, by 472 letters, and was the record for n = 13 on Oct 5, 2026, when W-0057 was 34 letters shorter.
- Length
- 6,747,917,498
- Repeated occurrences
- 1,693,434
- Announced
- Oct 5, 2026
0123456789ABC0123456789AB0C123456789AB01C23456789AB012C3456789AB0123C456789AB01234C56789AB012345C6789AB0123456C789AB0123…
Windows
| 6,747,917,486 | windows of 13 consecutive letters | |
| = | 6,227,020,800 | distinct permutations, all 13! of them |
| + | 1,693,434 | repeated occurrences of a permutation |
| + | 519,203,252 | windows that are not permutations |
How it was found
Relocation with re-opening took Halfar's 6,747,917,824 to 6,747,917,498 in under two hours; published first as a plan.
Checking
Total check time: 1 min 47 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 | 39 s |
| bitmapcheck | 288b3f67 | agrees, by Lehmer rank | 33 s |
| wordhash | 94925fe4 | the SHA-256 of the word and of its mirror | 34 s |
Download
Download Detour (.detour) 311.5 kB, or 6.7 GB decoded
# check it yourself
detour decode W-0054.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-0054.detour 6747917498
./target/release/bitmapcheck 13 ../W-0054.detour 6747917498
./target/release/wordhash 13 ../W-0054.detour 6747917498
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 54,124,090 tokens: 1 START, 1 literal of 1 byte in all, and 54,124,088 deviations. Deviations by weight, from 1 to 13: 1,693,434 · 15,240,194 · 37,187,822 · 932 · 462 · 358 · 429 · 200 · 55 · 66 · 60 · 55 · 21.