An update on the Linnik--Goldbach problem

Daniel R. Johnston; Tim Trudgian

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arXiv · 2605.17825

An update on the Linnik--Goldbach problem

Daniel R. Johnston·Tim Trudgian

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Abstract

We consider the Linnik--Goldbach problem of writing all large even integers as the sum of two primes and a fixed number of powers of 2. We show that, under the generalised Riemann hypothesis, one can use 6 powers of two. In addition, we discuss refinements to the unconditional case and to the related problem of Romanov in expressing a positive proportion of odd numbers as the sum of a prime and a power of 2.

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Daniel R. Johnston, Tim Trudgian. 2026-05-18. An update on the Linnik--Goldbach problem. https://arxiv.org/abs/2605.17825

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