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February 22, 2026Open Access

A Precision Prime Number Generator Based on Modular Distribution Statistics: From 8-Orbit Structure to Convergence Coefficient Locking

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Novel sieve method generates primes efficiently, indicating robustness and potential quantum applications.

This research aims to develop a prime number generator based on modular distribution statistics and convergence properties.
Developed a sieve based on modular distribution statistics using 8 residue classes modulo 30.
Applied stepwise sieving by counting residue frequencies and implementing a dynamic threshold.
Optimized algorithm for fully automatic sieving with a locked convergence coefficient at δ = 0.5.
Conducted experiments for large candidate sets (N=10^8) and analyzed prime proportions.
Achieved a candidate set with a prime proportion of 59% and minimal composites (0.18%).
Demonstrated consistent prime proportions across orbits, except for minor deviations in one orbit.
Established that convergence coefficient δ can vary without affecting candidate set size, showcasing robustness.
Compared favorably to the classical Sieve of Eratosthenes with lower computational load.

Huang Feiyue (2026) studied this question.

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February 22, 2026Open Access

View Full Paper

Ask AI

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Authors

Novel sieve method generates primes efficiently, indicating robustness and potential quantum applications.

This research aims to develop a prime number generator based on modular distribution statistics and convergence properties.
Developed a sieve based on modular distribution statistics using 8 residue classes modulo 30.
Applied stepwise sieving by counting residue frequencies and implementing a dynamic threshold.
Optimized algorithm for fully automatic sieving with a locked convergence coefficient at δ = 0.5.
Conducted experiments for large candidate sets (N=10^8) and analyzed prime proportions.
Achieved a candidate set with a prime proportion of 59% and minimal composites (0.18%).
Demonstrated consistent prime proportions across orbits, except for minor deviations in one orbit.
Established that convergence coefficient δ can vary without affecting candidate set size, showcasing robustness.
Compared favorably to the classical Sieve of Eratosthenes with lower computational load.

Huang Feiyue (2026) studied this question.

View Full Paper

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