The Lozan Method: A Gap-Based Approach to Enhanced Prime Discovery with Dynamic Weight Optimization Part 1

I present a systematic computational method for prime number discovery using gap-based arithmetic operations with empirically optimized lights. The Lozan method employsdynamic lighting of small offset operations around candidate numbers to enhance prime de-tection efficiency. Through comprehensive testing on multiple scales (103 to 107), I demon-strate measurable performance improvements over the baseline methods, achieving successrates of 26.3% in cryptographic prime generation tasks and showing a 7-16x enhancementover random sampling in various number ranges. The method exhibits consistent cross-scaleeffectiveness and provides practical applications in cryptographic key generation, algorithmicpreprocessing, and machine learning feature engineering. The method’s performance char-acteristics are analyzed, its effectiveness is validated through extensive empirical testing,and potential connections are explored to classical results in prime number theory.Keywords: Prime numbers, computational number theory, gap-based algorithms, primegeneration, cryptographic applications