English

Prime Holdout Problems

Number Theory 2023-07-19 v2 Computational Complexity

Abstract

This paper introduces prime holdout problems, a problem class related to the Collatz conjecture. After applying a linear function, instead of removing a finite set of prime factors, a holdout problem specifies a set of primes to be retained. A proof that all positive integers converge to 1 is given for both a finite and an infinite holdout problem. It is conjectured that finite holdout problems cannot diverge for any starting value, which has implications for divergent sequences in the Collatz conjecture.

Keywords

Cite

@article{arxiv.2205.12932,
  title  = {Prime Holdout Problems},
  author = {Max Milkert and Alex Ruchti and Josiah Yoder},
  journal= {arXiv preprint arXiv:2205.12932},
  year   = {2023}
}

Comments

7 pages, no figures

R2 v1 2026-06-24T11:28:43.974Z