An update on the Linnik--Goldbach and Romanov problems
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913137943379968 |
|---|---|
| author | Johnston, Daniel R. Trudgian, Tim |
| author_facet | Johnston, Daniel R. Trudgian, Tim |
| contents | 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 update the best known bounds on Romanov's constant, showing unconditionally that more than $25\%$ of odd numbers can be written as the sum of a prime and a power of 2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_17825 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An update on the Linnik--Goldbach and Romanov problems Johnston, Daniel R. Trudgian, Tim Number Theory 11N36, 11P32, 11M26, 11P55 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 update the best known bounds on Romanov's constant, showing unconditionally that more than $25\%$ of odd numbers can be written as the sum of a prime and a power of 2. |
| title | An update on the Linnik--Goldbach and Romanov problems |
| topic | Number Theory 11N36, 11P32, 11M26, 11P55 |
| url | https://arxiv.org/abs/2605.17825 |