The Optimus Markov Prime Conjecture:
A Probabilistic Model for
Approximating Prime Sequences
Version 1.33.7lulz, December 2025
Roble Mumin
Independent AI Researcher and AI Consultant
https://roblemumin.com
December 2025
Source:
1
Roble Mumin
Abstract
We introduce a hybrid probabilistic-analytic framework for simulating sequences
that approximate the primes. Our model combines empirical prime gap statistics
with a global feedback mechanism derived from the Prime Number Theorem to guide
the sequence toward the correct asymptotic density. Unlike traditional sieving or
primality-testing approaches, this method requires no factorization or primality checks
during simulation. A density ratio dynamically adjusts the local gap distribution to
enforce global consistency. Numerical experiments show that the resulting pseudo-prime
sequences reproduce both the local statistical irregularities and the global density
of true primes, with errors within approximately 1σof expected natural variations.
Furthermore, refined asymptotic approximations enable highly accurate forecasting
of prime positions, allowing efficient exact prime lookup via localized primality test-
ing—dramatically reducing compute for large-scale prime generation, with observed
speedups of 100–1,500×for accessiblenand effectively infinite for ultra-largen >10
9
.
Practical and Environmental Impact.
navigation approach in hashing, load balancing, sharding, and distributed systems could
yield substantial computational…打开文档引用此文档
Roble Mumin “Optimus Markov Prime Conjecture (v1.33.7lulz)”.
2025-12.
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current summary qualified; independent peer review not verified