Continued fractions with large prime partial quotients

Key Points

• The study identifies the Lebesgue measure and Hausdorff dimension for sets with large prime partial quotients.
• Findings include new asymptotics on the tail of the almost prime zeta function, enhancing previous research.
• This extend existing theorems by Łuczak and Huang-Wu-Xu, demonstrating further complexity in continued fractions.
• Results contribute to ongoing inquiries in number theory, with implications for understanding prime distributions.