Comptes Rendus
Théorie des nombres
On a conjecture of Erdős
Yong-Gao Chen1 ; Yuchen Ding2 
1 School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, People’s Republic of China
2 School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, People’s Republic of China
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 971-974.

In this note, we confirm an old conjecture of Erdős.

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DOI : 10.5802/crmath.345
Classification : 11A41, 11A67
Yong-Gao Chen 1 ; Yuchen Ding 2

1 School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, People’s Republic of China
2 School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, People’s Republic of China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Yong-Gao Chen; Yuchen Ding. On a conjecture of Erdős. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 971-974. doi : 10.5802/crmath.345. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.345/

[1] Yong-Gao Chen Romanoff theorem in a sparse set, Sci. China, Math., Volume 53 (2010) no. 9, pp. 2195-2202 | DOI | MR | Zbl

[2] Yong-Gao Chen; Xue-Gong Sun On Romanoff’s constant, J. Number Theory, Volume 106 (2004) no. 2, pp. 275-284 | DOI | MR | Zbl

[3] Yuchen Ding Extending an Erdős result on a Romanov type problem, Arch. Math., Volume 118 (2022), pp. 587-592 | DOI | MR | Zbl

[4] Yuchen Ding; G.-L. Zhou Some application of the admissible sets (preprint)

[5] Pál Erdős On integers of the form 2 k +p and some related problems, Summa Brasil. Math., Volume 2 (1950), pp. 113-123 | MR | Zbl

[6] Andrew Granville Primes in intervals of bounded length, Bull. Am. Math. Soc., Volume 52 (2015) no. 2, pp. 171-222 | DOI | MR | Zbl

[7] James Maynard Small gaps between primes, Ann. Math., Volume 181 (2015) no. 1, pp. 383-413 | DOI | MR | Zbl

[8] D. H. J. Polymath Variants of the Selberg sieve, and bounded intervals containing many primes, Res. Math. Sci., Volume 1 (2014), 12 | MR | Zbl

[9] Nikolaĭ P. Romanoff Über einige Sätze der additiven Zahlentheorie, Math. Ann., Volume 109 (1934), pp. 668-678 | DOI | Zbl

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