The Top 100

Researchers active on Legendre's conjecture and adjacent problems

Table Details

Columns

# overall rank (lower is better)
Name the researcher
Institution current affiliation
Ctry country
aX arXiv rank
OA OpenAlex rank
zM zbMATH rank
h h-index (citation impact)
Source databases that list them
YSP years since PhD (2026 minus the Math Genealogy PhD year; a dash when the PhD year is not known)

How it works. arXiv, OpenAlex and zbMATH each rank a researcher; the three ranks merge into one, weighted toward each person's strongest. Recent work counts more. Lower is better. Click any header to sort. A rank in [brackets] is an estimate, not measured. Full method.

#	Name	Institution		aX	OA	zM	h	Source	YSP
1	Kaisa Matomäki	University of Turku	FI	1	3	31	16	all_three	17
2	Janos Pintz	Alfréd Rényi Institute of Mathematics	HU	18	12	2	26	all_three	50
3	Terence Tao	University of California, Los Angeles	US	8	15	30	101	all_three	30
4	D. R. Heath-Brown	University of Oxford	GB	[25]	40	6	45	oa+zb	47
5	Daniel A. Goldston	San Jose State University	US	44	33	4	21	all_three	45
6	Glyn Harman	Royal Holloway University of London	GB	[26]	65	5	19	oa+zb	44
7	John B. Friedlander	University of Toronto	CA	[26]	48	8	34	oa+zb	54
8	Alessandro Zaccagnini	University of Parma	IT	5	21	83	14	all_three	32
9	Runbo Li	The High School Affiliated to Renmin University of China	CN	13	16	[47]	-	arx+oa	-
10	Alessandro Languasco	University of Padua	IT	6	14	112	12	all_three	30
11	Carl Pomerance	Dartmouth College	US	[27]	[83]	7	39	zb_only	54
12	James Maynard	University of Oxford	GB	12	83	17	11	all_three	13
13	K. Soundararajan	Stanford University	US	9	22	98	33	all_three	28
14	Ofir Gorodetsky	Technion - Israel Institute of Technology	IL	10	52	[48]	5	arx+oa	5
15	Brad Rodgers	Queen's University	CA	11	50	[48]	8	arx+oa	13
16	Henryk Iwaniec	Rutgers University	US	[29]	105	9	50	oa+zb	54
17	Joni Teräväinen	University of Cambridge	GB	7	11	162	9	all_three	8
18	Paul Pollack	University of Georgia	US	23	67	21	13	all_three	18
19	Jie Wu	Université Paris-Est Créteil Val-de-Marne	FR	49	69	14	19	all_three	36
20	Yu-Chen Sun	University of Turku	FI	16	[64]	[50]	-	arxiv_only	-
21	Etienne Fouvry	Université Paris-Saclay	FR	[30]	[76]	20	28	zb_only	45
22	Kevin Ford	University of Illinois Urbana-Champaign	US	24	[66]	28	-	arx+zb	32
23	Matt Visser	Victoria University of Wellington	NZ	20	56	[50]	-	arx+oa	42
24	Jiseong Kim	University of Mississippi	US	19	[64]	[50]	20	arxiv_only	3
25	Jesse Thorner	University of Illinois Urbana-Champaign	US	15	102	[50]	9	arx+oa	10
26	Roger C. Baker	Brigham Young University	US	68	93	12	34	all_three	55
27	Efrat Bank	Tel Aviv University	IL	22	[64]	[50]	3	arxiv_only	11
28	Andrew Granville	Université de Montréal	CA	58	39	26	32	all_three	39
29	Stephan Baier	Ramakrishna Mission Vivekananda Educational and Research Institute	IN	25	89	33	14	all_three	26
30	Adrian Dudek	University of Queensland	AU	17	46	121	5	all_three	10
31	Alberto Perelli	University of Genoa	IT	60	32	35	20	all_three	50
32	Harold G. Diamond	University of Illinois Urbana-Champaign	US	[28]	[68]	34	19	zb_only	61
33	Bingrong Huang	Shandong University	CN	33	64	[48]	7	arx+oa	9
34	Jörg Brüdern	University of Göttingen	DE	[28]	[68]	39	19	zb_only	38
35	Chaohua Jia	Chinese Academy of Sciences	CN	[32]	175	23	11	oa+zb	39
36	Vivian Kuperberg	ETH Zurich	CH	26	47	126	3	all_three	4
37	Xuancheng Shao	University of Kentucky	US	27	108	[53]	10	arx+oa	12
38	Zeev Rudnick	Tel Aviv University	IL	28	106	[52]	32	arx+oa	36
39	Jerzy Kaczorowski	Adam Mickiewicz University in Poznań	PL	[28]	[69]	42	19	zb_only	43
40	William D. Banks	University of Missouri	US	39	45	66	21	all_three	32
41	Sergey Konyagin	Steklov Mathematical Institute	RU	29	87	71	28	all_three	44
42	Cameron L. Stewart	University of Waterloo	CA	[28]	[69]	44	20	zb_only	50
43	Alexandru Zaharescu	University of Illinois Urbana-Champaign	US	31	57	109	24	all_three	35
44	Angel Kumchev	Towson University	US	40	[66]	48	12	arx+zb	25
45	Jori Merikoski	University of Helsinki	FI	21	109	94	2	all_three	5
46	Adolf Hildebrand	University of Illinois Urbana-Champaign	US	[28]	[69]	46	19	zb_only	43
47	Adam J. Harper	University of Warwick	GB	41	[64]	[50]	12	arxiv_only	14
48	Helmut Maier	Universität Ulm	DE	[28]	86	45	18	oa+zb	45
49	Sun-Kai Leung	University of Oxford	GB	35	123	[50]	1	arx+oa	1
50	Guangshi Lü	Shandong University	CN	[26]	51	64	17	oa+zb	22
51	J. P. Keating	University of Oxford	GB	48	[64]	[50]	40	arxiv_only	37
52	Michael Th. Rassias	Hellenic Military Academy	GR	34	38	188	24	all_three	12
53	Hugh Lowell Montgomery	University of Michigan	US	[28]	111	49	32	oa+zb	54
54	Wenguang Zhai	China University of Mining and Technology (Beijing)	CN	[26]	54	84	13	oa+zb	30
55	Hongze Li	Shanghai Jiao Tong University	CN	[28]	[76]	55	-	zb_only	36
56	Edva Roditty-Gershon	University of Bristol	GB	51	[64]	[50]	-	arxiv_only	11
57	D. Bazzanella	Politecnico di Torino	IT	[28]	84	57	-	oa+zb	30
58	Cem Yalçın Yıldırım	Boğaziçi University	TR	74	159	40	2	all_three	36
59	Andrés Chirre	Pontificia Universidad Católica del Perú	PE	52	120	[53]	5	arx+oa	7
60	M. B. Milinovich	University of Mississippi	US	54	112	[52]	11	arx+oa	18
61	Emmanuel Kowalski	ETH Zurich	CH	[31]	177	51	29	oa+zb	28
62	Tristan Freiberg	University of Waterloo	CA	30	156	118	4	all_three	16
63	Jianya Liu	Shandong University	CN	[28]	[76]	69	14	zb_only	31
64	Christian Axler	Heinrich Heine University Düsseldorf	DE	[32]	165	56	5	oa+zb	13
65	Ethan Smith	-	US	66	[64]	[50]	-	arxiv_only	17
66	Antal Balog	Alfréd Rényi Institute of Mathematics	HU	[32]	174	60	18	oa+zb	35
67	Yoichi Motohashi	Nihon University	JP	72	178	50	19	all_three	-
68	Hao Pan	Nanjing University of Finance and Economics	CN	[32]	181	61	17	oa+zb	20
69	S. Salerno	University of Salerno	IT	[28]	[76]	78	-	zb_only	-
70	Alexei Kourbatov	Independent	US	62	[74]	107	4	arx+zb	-
71	Chantal David	Concordia University	CA	75	[64]	[50]	14	arxiv_only	33
72	Fred B. Holt	Independent	US	[28]	[76]	81	6	zb_only	30
73	Trevor D. Wooley	Purdue University West Lafayette	US	67	[74]	117	28	arx+zb	36
74	Régis de la Bretèche	Université Paris Cité	FR	53	103	158	14	all_three	30
75	Victor Zhenyu Guo	Xi'an Jiaotong University	CN	[29]	[69]	89	4	zb_only	9
76	M. N. Huxley	Cardiff University	GB	[31]	173	76	23	oa+zb	56
77	Aled Walker	Kings College London	GB	73	161	[50]	-	arx+oa	8
78	S. W. Graham	Central Michigan University	US	[29]	[69]	101	15	zb_only	49
79	Timothy S. Trudgian	UNSW Canberra	AU	[30]	[69]	104	13	zb_only	16
80	P. Moree	Max Planck Institute for Mathematics	DE	[28]	[84]	120	20	zb_only	33
81	A. H. Ledoan	University of Tennessee at Chattanooga	US	[30]	117	155	-	oa+zb	19
82	Emre Alkan	Koç University	TR	[29]	[85]	129	13	zb_only	23
83	Greg Martin	University of British Columbia	CA	[30]	[86]	135	16	zb_only	29
84	Minggao Lu	Shanghai University	CN	[30]	[86]	142	3	zb_only	-
85	Ben Green	University of Oxford	GB	[30]	[86]	144	5	zb_only	23
86	Michaela Cully-Hugill	-	AU	[31]	152	140	3	oa+zb	3
87	Qi Yao	Dalhousie University	CA	[28]	[54]	184	-	zb_only	-
88	Feng Zhao	North China University of Water Resources and Electric Power	CN	[30]	[52]	199	-	zb_only	-
89	Efthymios Sofos	University of Rome Tor Vergata	IT	[30]	[52]	200	7	zb_only	11

Source column legend

The Source column records which of the pipelines ranked each researcher directly.

all_three: ranked directly by arXiv, OpenAlex, and zbMATH. The unanimous core.
arx+oa: ranked by arXiv and OpenAlex, but not zbMATH.
arx+zb: ranked by arXiv and zbMATH, but not OpenAlex.
oa+zb: ranked by OpenAlex and zbMATH, but not arXiv.
arxiv_only: ranked only by the arXiv pipeline.
oa_only: ranked only by OpenAlex. Often senior figures who publish in journals and do not post preprints.
zb_only: ranked only by zbMATH. Often pre-1995 Russian and Chinese number theorists.

Source	Count
`all_three`	26
`zb_only`	22
`oa+zb`	17
`arx+oa`	12
`arxiv_only`	8
`arx+zb`	4

Limitations

This list reflects publication output and citation network density, not subjective importance. A starting point, not a verdict.