# Smaller explicit prime digit-sum surjectivity threshold

Let `s_10(n)` be the decimal digit sum. This package certifies:

```text
M = 138033986655720044641496559943864
```

For every integer `m >= M` with `gcd(m, 9) = 1`, there is a prime
`p <= 10^(2m/9)` with `s_10(p) = m`.

The previous explicit published value in Lehmann
arXiv:2606.04677v1 is:

```text
177843590339381623423137292296355
```

Run the complete replay from the repository root:

```sh
uv run --frozen python \
  scratch/adjacent-unconditional--lehmann-prime-digit-sum-surjectivity-threshold/verify_all.py
```

The wrapper runs the primary Python-FLINT certificate at 256, 384,
and 512 bits, a separate Julia/Nemo reconstruction, and the pinned
author-code corroboration. Saved transcripts are compared byte for
byte.
