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	5	30	16	all_three	17
2	Janos Pintz	Alfréd Rényi Institute of Mathematics	HU	19	12	2	26	all_three	50
3	Glyn Harman	Royal Holloway University of London	GB	[26]	34	5	19	oa+zb	44
4	D. R. Heath-Brown	University of Oxford	GB	[26]	32	6	45	oa+zb	47
5	Terence Tao	University of California, Los Angeles	US	8	29	28	101	all_three	30
6	Daniel A. Goldston	San Jose State University	US	48	33	4	21	all_three	45
7	Alessandro Zaccagnini	University of Parma	IT	6	13	85	14	all_three	32
8	John B. Friedlander	University of Toronto	CA	[27]	51	8	34	oa+zb	54
9	Runbo Li	The High School Affiliated to Renmin University of China	CN	13	18	[49]	-	arx+oa	-
10	Alessandro Languasco	University of Padua	IT	7	11	112	12	all_three	30
11	Joni Teräväinen	University of Cambridge	GB	5	17	118	9	all_three	8
12	James Maynard	University of Oxford	GB	12	72	17	11	all_three	13
13	Henryk Iwaniec	Rutgers University	US	[28]	75	9	50	oa+zb	54
14	Jie Wu	Université Paris-Est Créteil Val-de-Marne	FR	53	25	14	19	all_three	36
15	K. Soundararajan	Stanford University	US	9	23	100	33	all_three	28
16	Ofir Gorodetsky	Technion - Israel Institute of Technology	IL	10	57	[54]	5	arx+oa	5
17	Etienne Fouvry	University of Paris-Saclay	FR	[27]	[53]	20	28	zb_only	45
18	Brad Rodgers	Queen's University	CA	11	66	[54]	8	arx+oa	13
19	Carl Pomerance	Dartmouth College	US	[28]	147	7	39	oa+zb	54
20	Jesse Thorner	University of Illinois Urbana-Champaign	US	16	50	[54]	9	arx+oa	10
21	Jiseong Kim	University of Mississippi	US	15	[60]	[51]	1	arxiv_only	3
22	Paul Pollack	University of Georgia	US	25	70	21	13	all_three	18
23	Chaohua Jia	Chinese Academy of Sciences	CN	[26]	[51]	24	11	zb_only	39
24	Yu-Chen Sun	University of Turku	FI	17	[60]	[51]	-	arxiv_only	-
25	Roger C. Baker	Brigham Young University	US	72	69	12	23	all_three	55
26	Kevin Ford	University of Illinois Urbana-Champaign	US	26	[56]	29	-	arx+zb	32
27	Andrew Granville	Université de Montréal	CA	63	26	27	32	all_three	39
28	Alberto Perelli	University of Genoa	IT	65	28	35	20	all_three	50
29	Adrian Dudek	University of Queensland	AU	18	48	122	5	all_three	10
30	Efrat Bank	Tel Aviv University	IL	23	76	[54]	3	arx+oa	11
31	Harold G. Diamond	University of Illinois Urbana-Champaign	US	[27]	[53]	34	19	zb_only	61
32	Stephan Baier	Ramakrishna Mission Vivekananda Educational and Research Institute	IN	27	94	33	14	all_three	26
33	Mayank Pandey	Princeton University	US	28	[60]	[51]	-	arxiv_only	-
34	Tristan Freiberg	University of Waterloo	CA	20	77	82	4	all_three	16
35	Jörg Brüdern	University of Göttingen	DE	[27]	[53]	39	19	zb_only	38
36	Matt Visser	Victoria University of Wellington	NZ	21	127	[54]	-	arx+oa	42
37	Wenguang Zhai	China University of Mining and Technology (Beijing)	CN	[26]	35	87	13	oa+zb	30
38	Sun-Kai Leung	University of Oxford	GB	29	82	[54]	1	arx+oa	1
39	Jerzy Kaczorowski	Adam Mickiewicz University in Poznań	PL	[27]	[55]	42	19	zb_only	43
40	Sergey Konyagin	Steklov Mathematical Institute	RU	33	55	72	28	all_three	44
41	Cameron L. Stewart	University of Waterloo	CA	[27]	[55]	44	20	zb_only	50
42	Alexandru Zaharescu	University of Illinois Urbana-Champaign	US	34	44	92	24	all_three	35
43	Guangshi Lü	Shandong University	CN	[27]	43	65	17	oa+zb	22
44	Adolf Hildebrand	University of Illinois Urbana-Champaign	US	[27]	[55]	46	19	zb_only	43
45	Bingrong Huang	Shandong University	CN	36	73	[54]	7	arx+oa	9
46	Jori Merikoski	University of Helsinki	FI	22	98	96	2	all_three	5
47	Xuancheng Shao	University of Kentucky	US	31	121	[54]	10	arx+oa	12
48	Vivian Kuperberg	ETH Zurich	CH	30	60	127	3	all_three	4
49	Zeev Rudnick	Tel Aviv University	IL	32	126	[54]	32	arx+oa	36
50	Angel Kumchev	Towson University	US	44	[58]	48	12	arx+zb	25
51	Helmut Maier	University of Ulm	DE	[27]	93	45	18	oa+zb	45
52	Cem Yalçın Yıldırım	Boğaziçi University	TR	78	[56]	40	2	arx+zb	36
53	Emmanuel Kowalski	ETH Zurich	CH	[27]	[55]	52	29	zb_only	28
54	Adam J. Harper	University of Warwick	GB	45	[60]	[51]	12	arxiv_only	14
55	Hongze Li	Shanghai Jiao Tong University	CN	[27]	[55]	53	-	zb_only	36
56	William D. Banks	University of Missouri	US	43	65	60	21	all_three	32
57	Hugh Lowell Montgomery	University of Michigan	US	[27]	96	50	32	oa+zb	54
58	J. P. Keating	University of Oxford	GB	52	[60]	[51]	40	arxiv_only	37
59	D. Bazzanella	Politecnico di Torino	IT	[27]	68	58	-	oa+zb	30
60	Edva Roditty-Gershon	University of Bristol	GB	55	[60]	[51]	-	arxiv_only	11
61	Yoichi Motohashi	Nihon University	JP	76	[58]	51	19	arx+zb	-
62	Hao Pan	Nanjing University of Finance and Economics	CN	[28]	[60]	62	17	zb_only	20
63	Michael Th. Rassias	Hellenic Military Academy	GR	39	49	188	24	all_three	12
64	Christian Axler	Heinrich Heine University Düsseldorf	DE	[29]	134	57	5	oa+zb	13
65	Jianya Liu	Shandong University	CN	[28]	[60]	70	19	zb_only	31
66	Antal Balog	Alfréd Rényi Institute of Mathematics	HU	[30]	143	61	18	oa+zb	35
67	Andrés Chirre	Pontificia Universidad Católica del Perú	PE	56	150	[54]	5	arx+oa	7
68	Ethan Smith	-	US	70	[60]	[51]	-	arxiv_only	17
69	M. B. Milinovich	University of Mississippi	US	59	136	[56]	11	arx+oa	18
70	Fred B. Holt	Independent	US	[28]	[60]	78	6	zb_only	30
71	S. Salerno	University of Salerno	IT	[28]	[60]	79	-	zb_only	-
72	Aled Walker	Kings College London	GB	77	[60]	[51]	-	arxiv_only	8
73	Alexei Kourbatov	Independent	US	67	[62]	109	4	arx+zb	-
74	Victor Zhenyu Guo	Xi'an Jiaotong University	CN	[28]	[60]	84	4	zb_only	9
75	Chantal David	Concordia University	CA	79	[60]	[51]	14	arxiv_only	33
76	M. N. Huxley	Cardiff University	GB	[30]	130	76	23	oa+zb	56
77	Régis de la Bretèche	Université Paris Cité	FR	58	91	160	14	all_three	30
78	S. W. Graham	Central Michigan University	US	[32]	[60]	103	15	zb_only	49
79	Timothy S. Trudgian	UNSW Canberra	AU	[30]	[62]	106	13	zb_only	16
80	Trevor D. Wooley	Purdue University West Lafayette	US	71	141	119	28	all_three	36
81	Michaela Cully-Hugill	-	AU	[29]	103	141	3	oa+zb	3
82	P. Moree	Max Planck Institute for Mathematics	DE	[28]	[60]	121	20	zb_only	33
83	Emre Alkan	Koç University	TR	[32]	[62]	130	13	zb_only	23
84	A. H. Ledoan	University of Tennessee at Chattanooga	US	[31]	120	157	-	oa+zb	19
85	Greg Martin	University of British Columbia	CA	[33]	[65]	136	16	zb_only	29
86	Minggao Lu	Shanghai University	CN	[32]	[65]	143	3	zb_only	-
87	Ben Green	University of Oxford	GB	[33]	[66]	145	5	zb_only	23
88	Qi Yao	Dalhousie University	CA	[26]	[48]	184	-	zb_only	-
89	Feng Zhao	North China University of Water Resources and Electric Power	CN	[30]	[54]	200	-	zb_only	-

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`	25
`zb_only`	23
`oa+zb`	15
`arx+oa`	12
`arxiv_only`	9
`arx+zb`	5

Limitations

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