Number Theory

    

A Characterization of Gaussian Compositeness in Arithmetic Progressions: A Generalized Rational Sieve

Authors: Jatin Dharkar

This paper introduces an algebraic sieve for identifying Gaussian primes within arithmetic progressions of the form N = ax + b. By mapping the primality of N onto a one-dimensional integer index x, we establish a parameterization x = (ap + b)n + p. We extend the domain of the parameters p and n to the field of Gaussian rationals Q(i), subject to specific integrality constraints on the resulting factors. We provide a formal proof of the sieve's completeness, demonstrating that the existence of a valid parameter pair (p, n) is both a necessary and sufficient condition for the compositeness of ax + b within the ring of Gaussian integers Z[i].

Comments: 4 Pages. (Note by viXra Admin: Please cite and listed scientific references)

Download: PDF

Submission history

[v1] 2026-07-25 02:18:45

Unique-IP document downloads: 0 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus