W-0057
A superpermutation on 13 symbols, found by Jakub Halfar. It beat the previous record, W-0054, by 34 letters, and was the record for n = 13 on Oct 5, 2026, when W-0059 was 43 letters shorter.
- Length
- 6,747,917,464
- Repeated occurrences
- 1,693,435
- Announced
- Oct 5, 2026
0123456789ABC0123456789AB0C123456789AB01C23456789AB012C3456789AB0123C456789AB01234C56789AB012345C6789AB0123456C789AB0123…
Windows
| 6,747,917,452 | windows of 13 consecutive letters | |
| = | 6,227,020,800 | distinct permutations, all 13! of them |
| + | 1,693,435 | repeated occurrences of a permutation |
| + | 519,203,217 | windows that are not permutations |
How it was found
Loop moves on the 6,747,917,498 word. Published only as a plan (plan/trailsearch-13-6747917464.plan). The plan is written against Halfar's 6,747,918,058 word, the base of his n = 13 plans on Pantone's selection; his tools/trailsearch.c rebuilds the word from that word and the plan.
Checking
Total check time: 1 min 56 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 | 42 s |
| bitmapcheck | 288b3f67 | agrees, by Lehmer rank | 35 s |
| wordhash | 94925fe4 | the SHA-256 of the word and of its mirror | 38 s |
Download
Download Detour (.detour) 312.8 kB, or 6.7 GB decoded
# check it yourself
detour decode W-0057.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-0057.detour 6747917464
./target/release/bitmapcheck 13 ../W-0057.detour 6747917464
./target/release/wordhash 13 ../W-0057.detour 6747917464
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 54,124,024 tokens: 1 START, 1 literal of 1 byte in all, and 54,124,022 deviations. Deviations by weight, from 1 to 13: 1,693,435 · 15,240,203 · 37,187,723 · 941 · 468 · 365 · 436 · 201 · 59 · 71 · 63 · 50 · 7.