Chronological Verification of the Collatz Conjecture using Theoretically Proven Sieves | ||
| Electronic Journal of Mathematical Analysis and Applications | ||
| Volume 13, Issue 1, 2025, Pages 1-10 PDF (236.87 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/ejmaa.2025.334871.1289 | ||
| Author | ||
| Samrat Dutta* | ||
| IBM, Bangalore, India | ||
| 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. | ||
| Keywords | ||
| Collatz Conjecture; Number Theory; Sieve; Parallal Computing; Algorithm | ||
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