415940

Chronological Verification of the Collatz Conjecture using Theoretically Proven Sieves

Article

Last updated: 09 Mar 2025

Subjects

-

Tags

Numerical optimization

Abstract

Lothar Collatz proposed a conjecture in number theory in 1937. The widely known Collatz conjecture has not been proven or disproven till date. It states that given any arbitary positive integer n, the function f (n), defined as n/2 if x is even and 3n + 1 if n is odd, generates a finite sequence that
eventually converges to the trivial cycle passing through the value of 1. There are several algorithmic approaches for verification of the conjecture. The sieve of Collatz is a new and popular algorithm to trace back the non linear problem to a linear cross back algorithm, speeding up the verification process. This paper presents a novel algorithmic approach to generate mathematically proven sieve bitsets of O(2^m) elements, where m ∈ N. The paper further presents a multi-core distributed approach for computational convergence verification of the Collatz conjecture using the pre-computed sieve. Our multi-threaded CPU implementation can verify 1.3 × 10^9 128-bit integers per second on Intel(R) Core(TM) i7-11850H CPU.

DOI

10.21608/ejmaa.2025.334871.1289

Keywords

Collatz Conjecture, Number Theory, sieve, Parallal Computing, Algorithm

Authors

First Name

Samrat

Last Name

Dutta

MiddleName

-

Affiliation

IBM, Bangalore, India

Email

samratduttaofficial@gmail.com

City

-

Orcid

0000-0002-4994-6919

Volume

13

Article Issue

1

Related Issue

51150

Issue Date

2025-01-01

Receive Date

2024-11-18

Publish Date

2025-01-01

Page Start

1

Page End

10

Print ISSN

3009-6731

Online ISSN

2090-729X

Link

https://ejmaa.journals.ekb.eg/article_415940.html

Detail API

http://journals.ekb.eg?_action=service&article_code=415940

Order

415,940

Type

Regular research papers

Type Code

2,651

Publication Type

Journal

Publication Title

Electronic Journal of Mathematical Analysis and Applications

Publication Link

https://ejmaa.journals.ekb.eg/

MainTitle

Chronological Verification of the Collatz Conjecture using Theoretically Proven Sieves

Details

Type

Article

Created At

09 Mar 2025