This repo stores Pratt certificates for primes in data/, with one certificate per file.

Certificates are plain text files with canonical line format:

V 1
P <prime>
W <witness>
F <factor>
F <factor>^<exponent>
...

Rules:

1. Exactly one P and one W line.
2. At least one F line.
3. Decimal integers only (canonical form, no leading zeroes).
4. Factors must be strictly ascending by factor base.
5. File must end with a trailing newline.

Each file name is a lowercase hex prefix (min length 16) of:

sha256(<prime-in-base-10>)

TIP contains the file id of the current top prime certificate.

Pull requests changing the prime number to a bigger one are welcome.

Verify the certificate pointed to by TIP:

nix run .#verify

Verify a specific certificate id:

nix run .#verify -- <id>

Verify a specific file path:

nix run .#verify -- data/<id>

What verification checks:

1. Certificate format and canonical constraints.
2. File id matches sha256(prime) prefix.
3. Direct dependency presence in data/ for every factor prime except 2.
4. Full Pratt math validation for the selected certificate.