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Abstract
By combining the sieve machinery used in the author's previous paper on this topic and some new arithmetic information in Harman's monograph, the author proves that the interval $[n-n^{\frac{1}{22}+\varepsilon}, n]$ contains prime numbers for almost all $n$, improving the previous exponent $\frac{1}{21.5}$ by the author. The use of the variable role-reversal plays a crucial role in the proof.
Supplementary materials
Title
Mathematica code for numerical calculations (1/2)
Description
This is the Mathematica code for the numerical calculations in the preprint.
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Title
Mathematica code for numerical calculations (2/2)
Description
This is the Mathematica code for the numerical calculations in the preprint.
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Title
Mathematica package SieveFunctions
Description
This is Galway's Mathematica package that gives values of functions FF(s) and ff(s) in our code.
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