Numerical verification of the Collatz conjecture for billion digit random numbers

TL;DR

This paper presents an algorithm capable of verifying the Collatz conjecture for numbers with up to ten billion digits using a standard PC, demonstrating computational feasibility for extremely large numbers.

Contribution

The paper introduces a practical algorithm that extends the verification of the Collatz conjecture to extremely large numbers with billions of digits.

Findings

Successfully verified the Collatz conjecture for numbers up to ten billion digits.

Demonstrated that the verification process is feasible on standard personal computers.

Provides a new computational approach for testing the conjecture on large-scale numbers.

Abstract

The Collatz conjecture, also known as the 3n+1 problem, is one of the most popular open problems in number theory. In this note, an algorithm for the verification of the Collatz conjecture is presented that works on a standard PC for numbers with up to ten billion decimal places.