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 dictated by a log log φ-weighted series.
Approximation by algebraic numbers, vol
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Continued fractions with large prime partial quotients
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 dictated by a log log φ-weighted series.