MIRЯIM
Prime-Engine Research
Experimental deterministic prime-navigation. The current MIRRIM line studies whether construction-style constraints can reduce prime search, with an RSA-4096 keygen benchmark as the public proof-of-concept.
Active research. Reproducible benchmarks under audit. Not a settled complexity theorem.
RSA-4096 Keygen Benchmark
Wall-clock comparison on the same hardware (n=200 keypairs, ~10-year-old laptop). MIRRIM uses 64 Miller-Rabin rounds; OpenSSL uses its FIPS 186-5 default (3 rounds for 4096-bit).
(64 MR rounds)
genrsa(FIPS-default 3 MR rounds)
done by MIRRIM
(success rate 100%)
Wall-Clock Lift, Honestly Framed
~½ the wall-clock time of OpenSSL's default RSA-4096 keygen, while running 64 Miller-Rabin rounds vs OpenSSL's 3. The lift is real; the comparison is not "same security" — it's "same hardware, MIRRIM doing more primality work."
Conservative Round Count
64-round Miller-Rabin pushes the false-positive rate well below FIPS minimums. Useful for high-assurance contexts; not the default-security regime OpenSSL ships with.
Reproducible Benchmark
Comparison code lives at MIRRIM_Safe_further_testing/benchmark_fair_comparison.py. n=200 keypair sample. Results vary with hardware; the structural ordering (MIRRIM faster while doing more rounds) holds.
GMP Hot Path
Built on gmpy2 (CPython binding to GNU Multiple Precision). The implementation lift over OpenSSL's BIGNUM at this size class is the standard GMP-vs-BN difference, surfaced through a clean Python wrapper.
No Pre-Computation Tricks
Each keypair generates fresh primes. No pre-computed tables, no shared seeds, no cached candidates. The benchmark numbers reflect from-scratch generation under the standard RSA-4096 spec.
Under Audit
The MIRRIM line is an active research project, not a settled complexity result. Wall-clock benchmarks are bounded measurements; they do not by themselves prove an asymptotic speedup over standard prime-search.
Benchmark Detail
RSA-4096 keypair generation, n=200, single thread, ~10-year-old laptop hardware.
64 MR rounds
genrsa3 MR rounds (default)
MIRRIM does
(200/200 keys)
Round-count source: OpenSSL 3.x sets BN_prime_checks_for_size(b) to 3 for primes ≥ 3747 bits (FIPS 186-5 compliant; bn.h in OpenSSL ≥ 3.0). MIRRIM was set to 64 rounds for this benchmark, giving error probability below 2⁻¹²⁸.
What the lift is and isn't: the wall-clock advantage at this size class comes from GMP's big-integer arithmetic via gmpy2 vs OpenSSL's BIGNUM. It is an implementation result. It does not by itself establish that the deterministic-navigation approach beats probabilistic prime-search asymptotically — that's a separate research question MIRRIM's broader bounded-benchmark work is investigating.
How to reproduce: the comparison harness lives in the MIRRIM-Safe further-testing directory. The harness runs both implementations on the same hardware, same RSA bit size, same n. Variance is high in any single run — the structural ordering (MIRRIM faster despite more MR rounds) is what holds across samples.
The Mathematics
Where the constructive prime line currently stands:
MIRRIM Prime Engine
Active deterministic-navigation research using Four Locks diagnostics and bounded benchmark maps. The live work is measuring where the construction helps and where it remains ordinary search.
Large Prime Generation
The pipeline has generated and verified primes with 10,000+ decimal digits — well past practical RSA sizes. This demonstrates that the method scales; it does not by itself prove an asymptotic advantage.
Cunningham Chains
Length-11 Cunningham chains generated as part of structural exploration. Length-11 chains are not records — the longest known chain (1st kind) is length 19 (since 2008) — but they are useful test material for the navigation primitives.
Cross-Domain Structure
The Four Locks share structure with the consent-gate operator we describe across the constellation work. Calling this a "morphism" is a research hypothesis, not a peer-reviewed theorem; it sits in the wider Velisyl Constellation programme.
The RSA benchmark is a proof-of-concept. The mathematics is the point — and the mathematics is still an open research line.
Open Research
This is active mathematical research. The prime-engine claims are experimental and remain under audit. The cross-domain connections to consent-gated collapse are presented as structural hypotheses, not peer-reviewed theorems. The RSA benchmark demonstrates implementation behaviour on a specific hardware sample. The mathematics is open for verification. Truth over comfort. Always.
Research Inquiry
Interested in MIRRIM prime-engine research, the Four Locks framework, or the wider consent-gated collapse programme connecting these to materials science, governance, and AI alignment? Get in touch — this is research-collaboration territory, not a product.
Open a conversationor email: shiraniabranches@gmail.com
Research Directions
Constructive Prime Theory
Building primes through structural conditions rather than rejection-sampling. The Four Locks act as consent-gate-style filters on number-theoretic candidates.
Cunningham Chains
Structural relationships between primes — chains where each element connects to the next through deterministic linear maps. Useful test surface for navigation primitives.
Cross-Domain Structure
The same consent-gate operator surfaces across number theory, materials science, game design, and other substrates in the Velisyl Constellation work. The cross-domain claim is a structural hypothesis under continuing audit.
Applied Cryptography (PoC)
RSA-4096 keygen as a public, reproducible benchmark for the navigation primitives. The PoC shows the implementation behaves; it does not on its own prove an algorithmic advantage at scale.
Large Prime Generation
10,000+ decimal-digit primes generated and verified. Demonstrates the pipeline scales past RSA-relevant sizes; does not establish an asymptotic complexity claim.
Foundations
Whether "factorization applied to ethics" is a true morphism between the consent-gate operator and number-theoretic structure is an open hypothesis we are continuing to test, not a settled theorem.