Recent papers

Recent papers on Landau's problems on prime numbers, surfaced by the prominence of their authors in this directory.

Showing 15 papers, ranked by the Top 100 standing of their authors then by recency. Authors who appear in the Top 100 are shown in bold.

#	Title	Authors	Published	Best rank
1	The average number of representations of an integer as a sum of two prime powers over multiples of a fixed integer	Alessandra Migliaccio, Alessandro Zaccagnini	2026-03	#4
2	Rough numbers between consecutive primes	Ayla Gafni, Terence Tao	2025-08	#8
3	Diophantine approximation with primes from short intervals	Stephan Baier, Sayantan Roy	2025-12	#17
4	Jacob's ladders and the equivalent of the Fermat-Wiles theorem generated by the Hardy-Littlewood formula (1921)	Jan Moser	2026-03	#27
5	Jacob's ladders, our asymptotic formulae (1981) and next $ζ$-equivalents of the Fermat-Wiles theorem together with decomposition and synthesis of the Riemann's $ζ$-oscillators	Jan Moser	2025-08	#27
6	Theorem $(1+1.9)$ on the Goldbach Conjecture	Jiamin Li, Jianya Liu	2026-06	#30
7	Estimating the tail of the singular product in the multivariate Bateman-Horn conjecture	Victor Volfson	2026-04	#34
8	The Exceptional Set in Goldbach's Problem with two Chen Primes	Lasse Grimmelt, Joni Teräväinen	2025-08	#36
9	Rational points on varieties defined by multihomogeneous diagonal forms	Doyon Kim, Tian Wang	2025-07	#37
10	On the exceptional set in the $abc$ conjecture	Runbo Li	2025-06	#43
11	Beyond the square-root barrier: cubic forms of Perazzo type	Tim Browning, Ritabrata Munshi, Victor Y. Wang	2026-04	#54
12	Strict Log-concavity of $k$-coloured Partitions	Kathrin Bringmann, Ben Kane, Anubhab Pahari, Larry Rolen	2025-10	#59
13	The reverse Goldbach problem and a refined Zsiflaw--Legeis theorem	Michael Harm, Daniel R. Johnston	2026-05	#64
14	An update on the Linnik--Goldbach and Romanov problems	Daniel R. Johnston, Tim Trudgian	2026-05	#64
15	Primes and almost primes between cubes	Daniel R. Johnston, Jonathan P. Sorenson, Simon N. Thomas, Jonathan E. Webster	2026-01	#64

Most cited (all time)

The ten most-cited Mathematics works on Landau's problems on prime numbers, by citation count in OpenAlex. Results are filtered to the Mathematics field (OpenAlex field 26) and ranked by total citations.

The Top 100 ranking is designed to capture prominent, currently active researchers. If an author in this table is not linked to a profile, it is usually because they are deceased or less active than the researchers in the ranking, not because they are less significant to the field.

#	Title	Authors	Year	Citations
1	Bounded gaps between primes DOI	Zhang Yitang	2014	463
2	Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4⋅10¹⁸ DOI	Tomás Oliveira e Silva; Siegfried Herzog; Silvio Pardi	2013	165
3	The ternary Goldbach conjecture is true DOI	H. A. Helfgott	2013	99
4	Verifying the Goldbach conjecture up to 4⋅10¹⁴ DOI	J. Richstein	2000	64
5	Irregularities in the distribution of primes and twin primes DOI	Richard P. Brent	1975	55
6	Average twin prime conjecture for elliptic curves DOI	Antal Balog; Alina-Carmen Cojocaru; Chantal David	2011	50
7	Evaluation of Artin’s constant and the twin-prime constant DOI	John W. Wrench	1961	48
8	Chen's double sieve, Goldbach's conjecture and the twin prime problem DOI	Jie Wu	2004	47
9	Bounded gaps between primes with a given primitive root DOI	Paul Pollack	2014	39
10	On the Vinogradov bound in the three primes Goldbach conjecture DOI	Mengmeng Liu; Tianze Wang	2002	36