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	1	31	16	all_three	17
2	Janos Pintz	Alfréd Rényi Institute of Mathematics	HU	19	9	2	26	all_three	50
3	Terence Tao	University of California, Los Angeles	US	8	10	30	101	all_three	30
4	Daniel A. Goldston	San Jose State University	US	46	27	4	21	all_three	45
5	D. R. Heath-Brown	University of Oxford	GB	[26]	36	6	45	oa+zb	47
6	Florian Luca	Stellenbosch University	ZA	[26]	74	3	28	oa+zb	30
7	Alessandro Zaccagnini	University of Parma	IT	5	18	82	14	all_three	32
8	Glyn Harman	Royal Holloway University of London	GB	[26]	80	5	19	oa+zb	44
9	Alessandro Languasco	University of Padua	IT	6	11	112	12	all_three	30
10	Runbo Li	University of Michigan	US	14	14	[53]	-	arx+oa	-
11	Carl Pomerance	Dartmouth College	US	[29]	[74]	7	39	zb_only	54
12	James Maynard	University of Oxford	GB	13	60	17	11	all_three	13
13	John B. Friedlander	University of Toronto	CA	[28]	77	8	34	oa+zb	54
14	K. Soundararajan	Stanford University	US	9	25	98	33	all_three	28
15	Ofir Gorodetsky	Technion - Israel Institute of Technology	IL	10	45	[52]	5	arx+oa	5
16	Brad Rodgers	Queen's University	CA	11	42	[52]	8	arx+oa	13
17	Henryk Iwaniec	Rutgers University	US	[30]	94	9	50	oa+zb	54
18	Joni Teräväinen	University of Cambridge	GB	7	8	162	9	all_three	8
19	Kevin Ford	University of Illinois Urbana-Champaign	US	20	[59]	27	-	arx+zb	32
20	Matt Visser	Victoria University of Wellington	NZ	12	59	[56]	-	arx+oa	42
21	Paul Pollack	University of Georgia	US	25	58	21	13	all_three	18
22	Jie Wu	Centre National de la Recherche Scientifique	FR	52	61	14	19	all_three	21
23	Etienne Fouvry	Université Paris-Saclay	FR	[30]	[67]	20	28	zb_only	45
24	Jesse Thorner	University of Illinois Urbana-Champaign	US	16	92	[56]	9	arx+oa	10
25	Andrew Granville	Université de Montréal	CA	64	35	26	32	all_three	39
26	Jiseong Kim	University of Mississippi	US	21	[57]	[61]	20	arxiv_only	3
27	Adrian Dudek	University of Queensland	AU	18	40	120	5	all_three	10
28	Dieter Wolke	University of Freiburg	DE	[28]	[61]	32	-	zb_only	57
29	Efrat Bank	Tel Aviv University	IL	24	[57]	[61]	3	arxiv_only	11
30	Roger C. Baker	Brigham Young University	US	80	104	12	34	all_three	55
31	Chaohua Jia	Chinese Academy of Sciences	CN	[32]	125	23	11	oa+zb	39
32	Stephan Baier	Ramakrishna Mission Vivekananda Educational and Research Institute	IN	33	55	33	14	all_three	26
33	Yu-Chen Sun	University of Turku	FI	26	[57]	[61]	-	arxiv_only	5
34	Harold G. Diamond	University of Illinois Urbana-Champaign	US	[30]	[61]	34	19	zb_only	61
35	Christian Axler	Heinrich Heine University Düsseldorf	DE	17	141	56	5	all_three	13
36	Sergey Konyagin	Steklov Mathematical Institute	RU	22	76	71	28	all_three	44
37	Alberto Perelli	University of Genoa	IT	68	34	35	20	all_three	50
38	Vivian Kuperberg	ETH Zurich	CH	27	33	125	3	all_three	4
39	Bingrong Huang	Shandong University	CN	32	54	[55]	7	arx+oa	9
40	Jörg Brüdern	University of Göttingen	DE	[30]	[67]	39	19	zb_only	38
41	Xuancheng Shao	University of Kentucky	US	28	96	[56]	10	arx+oa	12
42	Zeev Rudnick	Tel Aviv University	IL	29	103	[56]	32	arx+oa	36
43	Jerzy Kaczorowski	Adam Mickiewicz University in Poznań	PL	[30]	[67]	42	19	zb_only	43
44	Guangshi Lü	Shandong University	CN	[28]	44	64	17	oa+zb	22
45	Alexandru Zaharescu	University of Illinois Urbana-Champaign	US	34	43	109	24	all_three	35
46	Cameron L. Stewart	University of Waterloo	CA	[30]	[67]	44	20	zb_only	50
47	Tristan Freiberg	University of Waterloo	CA	30	[58]	117	4	arx+zb	16
48	Jori Merikoski	University of Helsinki	FI	23	97	94	2	all_three	5
49	Helmut Maier	Universität Ulm	DE	[29]	75	45	18	oa+zb	45
50	Adolf Hildebrand	University of Illinois Urbana-Champaign	US	[30]	[67]	46	19	zb_only	43
51	Sun-Kai Leung	University of Oxford	GB	36	86	[56]	1	arx+oa	1
52	Angel Kumchev	Towson University	US	43	[62]	48	12	arx+zb	25
53	Wenguang Zhai	China University of Mining and Technology (Beijing)	CN	[28]	47	84	13	oa+zb	30
54	Victor Zhenyu Guo	Xi'an Jiaotong University	CN	37	[62]	89	4	arx+zb	9
55	Michael Th. Rassias	Hellenic Military Academy	GR	35	32	188	24	all_three	12
56	Hugh Lowell Montgomery	University of Michigan	US	[29]	91	49	32	oa+zb	54
57	Felix Sidokhine	Independent	CA	38	134	[56]	-	arx+oa	-
58	Hongze Li	Shanghai Jiao Tong University	CN	[30]	[73]	55	-	zb_only	36
59	J. P. Keating	University of Oxford	GB	50	[57]	[61]	40	arxiv_only	37
60	D. Bazzanella	Politecnico di Torino	IT	[29]	73	57	-	oa+zb	30
61	William D. Banks	University of Missouri	US	49	83	66	21	all_three	32
62	Edva Roditty-Gershon	University of Bristol	GB	55	[57]	[61]	-	arxiv_only	11
63	Emmanuel Kowalski	ETH Zurich	CH	[33]	152	51	29	oa+zb	28
64	Cem Yalçın Yıldırım	Boğaziçi University	TR	87	135	40	2	all_three	36
65	Jianya Liu	Shandong University	CN	[30]	[73]	69	14	zb_only	31
66	Régis de la Bretèche	Université Paris Cité	FR	40	93	158	14	all_three	30
67	M. B. Milinovich	University of Mississippi	US	59	99	[56]	11	arx+oa	18
68	Antal Balog	Alfréd Rényi Institute of Mathematics	HU	[34]	150	60	18	oa+zb	35
69	Alexei Kourbatov	Independent	US	58	[65]	107	4	arx+zb	-
70	Hao Pan	Nanjing University of Finance and Economics	CN	[35]	157	61	17	oa+zb	20
71	Yoichi Motohashi	Nihon University	JP	84	154	50	19	all_three	-
72	Andrés Chirre	Pontificia Universidad Católica del Perú	PE	56	166	[57]	5	arx+oa	7
73	S. Salerno	University of Salerno	IT	[30]	[73]	78	-	zb_only	-
74	Fred B. Holt	Independent	US	[30]	[73]	80	6	zb_only	30
75	Greg Martin	University of British Columbia	CA	63	[66]	134	16	arx+zb	29
76	Daniel Fiorilli	Centre National de la Recherche Scientifique	FR	76	[57]	[61]	9	arxiv_only	15
77	Chantal David	Concordia University	CA	77	[57]	[61]	14	arxiv_only	33
78	Ethan Smith	Northern Michigan University	US	78	[57]	[61]	-	arxiv_only	17
79	M. N. Huxley	Cardiff University	GB	[33]	149	76	23	oa+zb	56
80	Germán Paz	Independent	AR	82	[57]	[61]	-	arxiv_only	-
81	Trevor D. Wooley	Purdue University West Lafayette	US	79	[58]	116	28	arx+zb	36
82	S. W. Graham	Central Michigan University	US	[32]	[67]	101	15	zb_only	49
83	Aled Walker	Kings College London	GB	85	137	[57]	-	arx+oa	8
84	Timothy S. Trudgian	Australian National University	AU	[33]	[67]	104	13	zb_only	16
85	A. H. Ledoan	University of Tennessee at Chattanooga	US	[28]	105	155	-	oa+zb	19
86	P. Moree	Max Planck Institute for Mathematics	DE	[30]	[66]	119	20	zb_only	33
87	Emre Alkan	Koç University	TR	[32]	[73]	128	13	zb_only	23
88	Minggao Lu	Shanghai University	CN	[30]	[76]	142	3	zb_only	-
89	Ben Green	University of Oxford	GB	[32]	[76]	144	5	zb_only	23
90	Michaela Cully-Hugill	University of New South Wales	AU	[34]	158	139	3	oa+zb	3
91	Ian Richards	University of Minnesota	US	[30]	[42]	173	15	zb_only	66
92	Qi Yao	-	CN	[32]	[42]	184	-	zb_only	-
93	Feng Zhao	North China University of Water Resources and Electric Power	CN	[32]	[36]	198	-	zb_only	-
94	Efthymios Sofos	University of Glasgow	GB	[34]	[40]	199	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`	13
`arxiv_only`	9
`arx+zb`	7

Limitations

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