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.
Dutta, S. (2025). Chronological Verification of the Collatz Conjecture using Theoretically Proven Sieves. Electronic Journal of Mathematical Analysis and Applications, 13(1), 1-10. doi: 10.21608/ejmaa.2025.334871.1289
MLA
Samrat Dutta. "Chronological Verification of the Collatz Conjecture using Theoretically Proven Sieves", Electronic Journal of Mathematical Analysis and Applications, 13, 1, 2025, 1-10. doi: 10.21608/ejmaa.2025.334871.1289
HARVARD
Dutta, S. (2025). 'Chronological Verification of the Collatz Conjecture using Theoretically Proven Sieves', Electronic Journal of Mathematical Analysis and Applications, 13(1), pp. 1-10. doi: 10.21608/ejmaa.2025.334871.1289
VANCOUVER
Dutta, S. Chronological Verification of the Collatz Conjecture using Theoretically Proven Sieves. Electronic Journal of Mathematical Analysis and Applications, 2025; 13(1): 1-10. doi: 10.21608/ejmaa.2025.334871.1289
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