Identifies integers with limited prime factors in arithmetic progressions, suggesting new insights in number theory.
For all sufficiently large , in any arithmetic progression in which and are relatively prime there exists a positive integer with at most two prime factors (counted with multiplicity) which is asymptotically less than . The proof uses the weighted sieve of Greaves–Halberstam–Richert with bilinear remainder terms and Selberg's sieve.
No takes yet. Share an insight, caveat, or question.
Ha et al. (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: