Verification Pipeline Architecture
Sieve & PRP Screening
Candidates of the form (7^n - 2) are sieved locally using modular arithmetic up to (p = 10,000,000), eliminating ~92% of composite numbers.
Survivors are tested using OpenPFGW executing a 3-PRP test to establish probable primality.
Deterministic ECPP
For moderate exponents, confirmed PRPs are run through Primo (v4.3.3 LX64) executing Elliptic Curve Primality Proving[cite: 1].
Primo constructs a 100% mathematically rigorous proof certificate (`.out`) that can be independently validated.
Ultra-Large MR Certification
When candidate digit lengths exceed practical ECPP compute limits, numbers are certified to near-certainty via a multi-stage Miller-Rabin suite.
Evaluating (k) independent random bases reduces composite error probability to under (4^{-k}) (e.g., (1.6 \times 10^{-60}) for (k=100)).
Open-Source Python Certification Tools
To enable peer verification and auditability, the custom Python programs used for generating dual-stage Miller-Rabin tests and verifying audit trace logs are publicly available below:
Miller-Rabin Dual-Stage Tester
mr_cert_test.py
Independent Certificate Auditor
mr_cert_verification.py