An explicit version of Chen's theorem and the linear sieve

Daniel R. Johnston; Matteo Bordignon; Valeriia Starichkova

An explicit version of Chen's theorem and the linear sieve

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arxiv 2207.09452 v6 pith:MGLOXXYY submitted 2022-07-15 math.NT

Matteo Bordignon , Daniel R. Johnston , Valeriia Starichkova This is my paper · ORCID

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keywords chendrawingeveneveryexplicitinspirationintegerlarger

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abstract

Drawing inspiration from the work of Nathanson and Yamada we prove that every even integer larger than $\exp (\exp (32.7))$ can be written as the sum of a prime and the product of at most two primes.

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Continued fractions with large prime partial quotients
math.NT 2025-07 conditional novelty 7.0 of 10

For any growth function φ, the sets of reals whose product of ℓ consecutive prime partial quotients exceeds φ infinitely often have Hausdorff dimension equal to the unrestricted case, and zero-one Lebesgue measure dic...

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