On the Emergence of the Quanta Prime Sequence

TL;DR

This paper introduces the Quanta Prime Sequence (QPS), a new mathematical construct with deep connections to prime numbers, number theory, and cryptography, and explores its implications for primality testing and the Riemann Hypothesis.

Contribution

The paper presents the foundational theorem of QPS and demonstrates its relevance to various important sequences and primality tests, offering new insights and potential applications.

Findings

QPS relates to Mersenne, Fermat, Lucas, Fibonacci, Chebyshev, and Dickson sequences.

QPS has implications for the Lucas-Lehmer primality test.

A new link between QPS and the Harmonic series suggests progress towards the Riemann Hypothesis.

Abstract

This paper presents the Quanta Prime Sequence (QPS) and its foundational theorem, showcasing a unique class of polynomials with substantial implications. The study uncovers profound connections between Quanta Prime numbers and essential sequences in number theory and cryptography. The investigation highlights the sequence's contribution to the emergence of new primes and its embodiment of core mathematical constructs, including Mersenne numbers, Fermat numbers, Lucas numbers, Fibonacci numbers, the Chebyshev sequence, and the Dickson sequence. The comprehensive analysis emphasizes the sequence's intrinsic relevance to the Lucas-Lehmer primality test. This research positions the Quanta Prime sequence as a pivotal tool in cryptographic applications, offering novel representations of critical mathematical structures. Additionally, a new result linking the Quanta Prime sequence to the Harmonic series is introduced, hinting at potential progress in understanding the Riemann Hypothesis.