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On the Exceptional Set of the Sum of a Prime Number and a Fixed Degree of a Prime Number

Исмаил АллаковTermez State University, 43 Hodzhaeva str., Termez, 190111, Republic of UzbekistanA. Sh. SafarovTermez State University, 43 Hodzhaeva str., Termez, 190111, Republic of Uzbekistan

Russian Mathematicsjournal2020en

ABI

Аннотация

Let X be a sufficiently great real number and M denote the set of natural numbers not exceeding X which cannot be written as a sum of a prime and a fixed degree of a prime number from the arithmetical progression with difference d. Let Ed(X) = cardM. We obtain a new numerical degree estimate for the set Ed(X) and an estimate from below for the number of presentations of n ∉ M in the specified type. The proven estimates refine the generalization for an arithmetical progression of results earlier got by V.A. Plaksin.

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Analytic Number Theory Research History and Theory of Mathematics Algebraic Geometry and Number Theory

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DOI: 10.3103/s1066369x20010028

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