W-0020
A superpermutation on 13 symbols, found by Uku Raudvere. It was the first record for n = 13, and held it from Jul 27 until Sep 29, 2026, when W-0027 was 1,580,883 letters shorter.
- Length
- 6,749,568,009
- Repeated occurrences
- 0
- Announced
- Jul 27, 2026
0123456789ABC0123456789AB0C123456789AB01C23456789AB012C3456789AB0123C456789AB01234C56789AB012345C6789AB0123456C789AB0123…
Windows
| 6,749,567,997 | windows of 13 consecutive letters | |
| = | 6,227,020,800 | distinct permutations, all 13! of them |
| + | 0 | repeated occurrences of a permutation |
| + | 522,547,197 | windows that are not permutations |
How it was found
Egan's length minus 1 at n = 13, lifted from the n = 12 certificate; Raudvere published the certificate (lift/n13.sprc.xz) and a SHA-256 of the word, not the word.
Checking
| Program | Source | Result | Time |
|---|---|---|---|
| permcheck | c46d3654 | all 6,227,020,800 permutations appear | 6 min 21 s |
| literal_check | f4687121 | agrees on coverage | 16 min 12 s |
Download
Download Detour (.detour) 172.2 kB, or 6.7 GB decoded
# check it yourself
detour decode W-0020.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-0020.detour 6749568009
./target/release/bitmapcheck 13 ../W-0020.detour 6749568009
./target/release/wordhash 13 ../W-0020.detour 6749568009
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 522,547,083 tokens: 1 START, 1 literal of 1 byte in all, and 522,547,081 deviations. Deviations by weight, from 1 to 13: 0 · 522,547,073 · 8 · 0 · 0 · 0 · 0 · 0 · 0 · 0 · 0 · 0 · 0.