Finding Prime Numbers as Fixed Points of Sequences

TL;DR

This paper presents a novel method to identify prime numbers as fixed points of simple sequences, achieving over 99.9% success, and specifically relates odd primes to fixed points of a sequence involving divisors of triangular numbers.

Contribution

It introduces a new sequence-based approach to find primes as fixed points, linking prime identification to fixed points of sequences related to divisors of triangular numbers.

Findings

Success rate over 99.9% for prime identification

Primes can be characterized as fixed points of specific sequences

Odd primes correspond to fixed points of the sequence A(1)

Abstract

In this note we describe a method for finding prime numbers as fixed points of particularly simple sequences. Some basic calculations show that success rates for identifying primes this way are over 99.9%. In particular, it seems that the set of odd primes can be obtained as fixed points of the sequence which we call A(1), the sequence of smallest divisors of triangular numbers, where the divisors are positive numbers that have not yet appeared in the sequence.