Optimized Integral Controller Searching Prime Number Orders

TL;DR

This paper introduces an innovative integral controller that efficiently searches prime number sets using feedback control principles, inspired by PID tuning rules, ensuring predictable performance regardless of prime set size.

Contribution

It presents a novel application of integral control for prime number search, bridging control theory and number theory in an innovative way.

Findings

Efficient prime set search using integral control

Predictable performance independent of prime set size

Novel feedback control approach for number theory problems

Abstract

The concept of integration is generally applicable to automatic control of processes. As shown in this paper, integral controller performs efficient searches in the extensive prime sets, too. An inspiration by the simple analytic rules for PID controller tuning results in integral controller that ensures predictable work regardless of the cardinality of primes. It gives an innovative application of the feedback control which relates to a gradient method.