Recent papers

Recent papers on Legendre's conjecture, surfaced by the prominence of their authors in this directory.

Showing 14 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	A weaker but simpler sieve inequality	John B. Friedlander	2026-07	#7
2	On the largest prime factor of integers in short intervals III	Runbo Li	2026-01	#9
3	Distribution of random multiplicative functions in short intervals, with proper normalization	Adam J. Harper, Kannan Soundararajan, Max Wenqiang Xu	2026-06	#13
4	Large sieve inequality for sums of Legendre symbols over short intervals	Marc Munsch, Igor Shparlinski, Yu-Chen Sun, Yixiu Xiao	2026-04	#20
5	Sierpinski's Hypothesis H1	Matt Visser	2025-12	#23
6	On Averages of Shifted Convolutions with Applications to $GL(2)$ and $GL(3)$ Fourier Coefficients	Jiseong Kim	2025-09	#24
7	Partial progress towards the large sieve for square moduli	Stephan Baier	2026-05	#29
8	Diophantine approximation with primes from short intervals	Stephan Baier, Sayantan Roy	2025-12	#29
9	Closed geodesics in short intervals for random hyperbolic surfaces	Zeev Rudnick	2026-05	#38
10	Unshared zeros of Dirichlet $L$-functions	William Banks, Kyle Loftus	2026-07	#40
11	On Sidon sets with squares, cubes and quartics in short intervals	M. Z. Garaev, F. M. Garayev, S. V. Konyagin	2026-02	#41
12	On Goldbach numbers in short intervals	Andrés Chirre, Markus Valås Hagen	2025-12	#59
13	Surviving Eratosthenes sieve I: quadratic density and Legendre's conjecture	Fred B. Holt	2026-03	#72
14	Piatetski-Shapiro Primes in short intervals	Lingyu Guo, Victor Zhenyu Guo	2026-05	#75

Most cited (all time)

The ten most-cited Mathematics works on Legendre's conjecture, 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	The Distribution of Prime Numbers DOI	Bouras, Mohammed	1933	473
2	Bounded gaps between primes DOI	Zhang Yitang	2014	466
3	The Difference Between Consecutive Primes, II DOI	Roger C. Baker; G. Harman; J. Pintz	2001	420
4	Small gaps between primes DOI	James Maynard	2014	311
5	On the order of magnitude of the difference between consecutive prime numbers DOI	Harald Cramér	1936	297
6	A heuristic asymptotic formula concerning the distribution of prime numbers DOI	Paul T. Bateman; Roger A. Horn	1962	267
7	On the difference between consecutive primes DOI	M. N. Huxley	1971	234
8	The Difference Between Consecutive Primes DOI	Roger C. Baker; G. Harman	1996	227
9	Prime Numbers in Short Intervals and a Generalized Vaughan Identity DOI	D. R. Heath‐Brown	1982	199
10	On the distribution of primes in short intervals DOI	P. X. Gallagher	1976	176