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	24	16	all_three	17
2	Janos Pintz	Alfréd Rényi Institute of Mathematics	HU	15	9	2	26	all_three	50
3	D. R. Heath-Brown	University of Oxford	GB	[23]	36	5	45	oa+zb	47
4	Alessandro Zaccagnini	University of Parma	IT	4	18	68	14	all_three	32
5	Florian Luca	Stellenbosch University	ZA	[24]	74	3	28	oa+zb	30
6	Alessandro Languasco	University of Padua	IT	5	11	94	12	all_three	30
7	Terence Tao	University of California, Los Angeles	US	[22]	10	[39]	101	oa_only	30
8	Glyn Harman	Royal Holloway University of London	GB	[24]	80	4	19	oa+zb	44
9	Runbo Li	University of Michigan	US	11	14	[54]	-	arx+oa	-
10	Carl Pomerance	Dartmouth College	US	[23]	[74]	6	39	zb_only	54
11	John B. Friedlander	University of Toronto	CA	[24]	77	7	34	oa+zb	54
12	K. Soundararajan	Stanford University	US	7	25	82	33	all_three	28
13	Henryk Iwaniec	Rutgers University	US	[24]	94	8	50	oa+zb	54
14	Joni Teräväinen	University of Cambridge	GB	6	8	141	9	all_three	8
15	Ofir Gorodetsky	Technion - Israel Institute of Technology	IL	8	45	[54]	5	arx+oa	5
16	Brad Rodgers	Queen's University	CA	9	42	[54]	8	arx+oa	13
17	Paul Pollack	University of Georgia	US	21	58	17	13	all_three	18
18	Kevin Ford	University of Illinois Urbana-Champaign	US	16	[67]	21	-	arx+zb	32
19	Andrew Granville	Université de Montréal	CA	55	35	20	32	all_three	39
20	Daniel A. Goldston	San Jose State University	US	[22]	27	[39]	21	oa_only	45
21	Stephan Baier	Ramakrishna Mission Vivekananda Educational and Research Institute	IN	29	55	26	14	all_three	26
22	Jesse Thorner	University of Illinois Urbana-Champaign	US	13	92	[57]	9	arx+oa	10
23	Jiseong Kim	University of Mississippi	US	17	[58]	[68]	20	arxiv_only	3
24	Harold G. Diamond	University of Illinois Urbana-Champaign	US	[24]	[75]	27	19	zb_only	61
25	Roger C. Baker	Brigham Young University	US	70	104	11	34	all_three	55
26	Alberto Perelli	University of Genoa	IT	[23]	34	[39]	20	oa_only	50
27	Efrat Bank	Tel Aviv University	IL	20	[58]	[68]	3	arxiv_only	11
28	Christian Axler	Heinrich Heine University Düsseldorf	DE	14	141	46	5	all_three	13
29	Vivian Kuperberg	ETH Zurich	CH	23	33	105	3	all_three	4
30	Bingrong Huang	Shandong University	CN	28	54	[56]	7	arx+oa	9
31	Helmut Maier	Universität Ulm	DE	[24]	75	35	18	oa+zb	45
32	Adolf Hildebrand	University of Illinois Urbana-Champaign	US	[24]	[76]	36	19	zb_only	43
33	Xuancheng Shao	University of Kentucky	US	24	96	[57]	10	arx+oa	12
34	Matt Visser	Victoria University of Wellington	NZ	10	59	195	-	all_three	42
35	Jori Merikoski	University of Helsinki	FI	19	97	78	2	all_three	5
36	Alexandru Zaharescu	University of Illinois Urbana-Champaign	US	[24]	43	[39]	24	oa_only	35
37	Guangshi Lü	Shandong University	CN	[24]	44	[39]	17	oa_only	22
38	Angel Kumchev	Towson University	US	37	[67]	38	12	arx+zb	25
39	Hugh Lowell Montgomery	University of Michigan	US	[24]	91	39	32	oa+zb	54
40	Tristan Freiberg	University of Waterloo	CA	26	[67]	99	4	arx+zb	16
41	Wenguang Zhai	China University of Mining and Technology (Beijing)	CN	[24]	47	[39]	13	oa_only	30
42	Sun-Kai Leung	University of Oxford	GB	31	86	[57]	1	arx+oa	1
43	Michael Th. Rassias	Hellenic Military Academy	GR	30	32	167	24	all_three	12
44	Régis de la Bretèche	Université Paris Cité	FR	34	93	[57]	14	arx+oa	30
45	D. Bazzanella	Politecnico di Torino	IT	[24]	73	47	-	oa+zb	30
46	Felix Sidokhine	Independent	CA	32	134	[54]	-	arx+oa	-
47	William D. Banks	University of Missouri	US	43	83	54	21	all_three	32
48	Cem Yalçın Yıldırım	Boğaziçi University	TR	77	135	31	2	all_three	36
49	Edva Roditty-Gershon	University of Bristol	GB	46	[58]	[68]	-	arxiv_only	11
50	Jianya Liu	Shandong University	CN	[23]	[75]	56	14	zb_only	31
51	James Maynard	University of Oxford	GB	[24]	60	[46]	11	oa_only	13
52	Antal Balog	Alfréd Rényi Institute of Mathematics	HU	[27]	150	50	18	oa+zb	35
53	M. B. Milinovich	University of Mississippi	US	50	99	[57]	11	arx+oa	18
54	Alexei Kourbatov	Independent	US	49	[67]	90	4	arx+zb	-
55	S. Salerno	University of Salerno	IT	[23]	[75]	64	-	zb_only	-
56	Zeev Rudnick	Tel Aviv University	IL	25	103	197	32	all_three	36
57	Fred B. Holt	Independent	US	[23]	[75]	66	6	zb_only	30
58	Yoichi Motohashi	Nihon University	JP	75	154	40	19	all_three	-
59	J. P. Keating	University of Oxford	GB	42	[59]	189	40	arx+zb	37
60	Andrés Chirre	Pontificia Universidad Católica del Perú	PE	47	166	[56]	5	arx+oa	7
61	Greg Martin	University of British Columbia	CA	54	[66]	114	16	arx+zb	29
62	Daniel Fiorilli	Centre National de la Recherche Scientifique	FR	66	[58]	[68]	9	arxiv_only	15
63	Chantal David	Concordia University	CA	67	[58]	[68]	14	arxiv_only	33
64	Ethan Smith	Northern Michigan University	US	68	[58]	[68]	-	arxiv_only	17
65	Germán Paz	Independent	AR	72	[58]	[68]	-	arxiv_only	-
66	S. W. Graham	Central Michigan University	US	[24]	[74]	85	15	zb_only	49
67	Aled Walker	Kings College London	GB	74	137	[54]	-	arx+oa	8
68	P. Moree	Max Planck Institute for Mathematics	DE	[25]	[75]	101	20	zb_only	33
69	Emre Alkan	Koç University	TR	[26]	[79]	108	13	zb_only	23
70	A. H. Ledoan	University of Tennessee at Chattanooga	US	[25]	105	134	-	oa+zb	19
71	Michaela Cully-Hugill	University of New South Wales	AU	[29]	158	119	3	oa+zb	3
72	Feng Zhao	North China University of Water Resources and Electric Power	CN	[24]	[59]	177	-	zb_only	-
73	Efthymios Sofos	University of Glasgow	GB	[24]	[59]	178	7	zb_only	11
74	Matti Jutila	University of Turku	FI	[26]	[59]	185	23	zb_only	56
75	Yuanyou Furui Cheng	Central Michigan University	US	[26]	[81]	196	-	zb_only	31

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`	19
`zb_only`	13
`arx+oa`	12
`oa+zb`	11
`oa_only`	7
`arxiv_only`	7
`arx+zb`	6

Limitations

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