The Top 100

Researchers active on Goldbach, twin primes, Legendre's conjecture, n2+1 primes, sieve methods, and the analytic techniques shared across Landau's four 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	Janos Pintz	Alfréd Rényi Institute of Mathematics	HU	1	6	2	26	all_three	50
2	Daniel A. Goldston	San Jose State University	US	[15]	9	[40]	21	oa_only	45
3	Terence Tao	University of California, Los Angeles	US	[15]	11	[40]	101	oa_only	30
4	Joni Teräväinen	University of Cambridge	GB	2	16	115	9	all_three	8
5	Alessandro Zaccagnini	University of Parma	IT	5	[88]	19	14	arx+zb	32
6	Jinjiang Li	China University of Mining and Technology (Beijing)	CN	14	17	34	6	all_three	-
7	Kaisa Matomäki	University of Turku	FI	6	45	40	16	all_three	17
8	Paul Pollack	University of Georgia	US	18	46	25	13	all_three	18
9	Glyn Harman	Royal Holloway University of London	GB	[48]	[83]	7	19	zb_only	44
10	Alessandro Languasco	University of Padua	IT	11	130	11	12	all_three	30
11	Trevor D. Wooley	Purdue University West Lafayette	US	16	34	54	28	all_three	36
12	Vivian Kuperberg	ETH Zurich	CH	12	69	[44]	3	arx+oa	4
13	D. R. Heath-Brown	University of Oxford	GB	59	86	6	45	all_three	47
14	Kevin Ford	University of Illinois Urbana-Champaign	US	13	[88]	41	-	arx+zb	32
15	Min Zhang	Beijing Information Science and Technology University	CN	15	[88]	35	44	arx+zb	-
16	Stephan Baier	Ramakrishna Mission Vivekananda Educational and Research Institute	IN	34	133	10	14	all_three	26
17	Gérald Tenenbaum	Institut Élie Cartan de Lorraine	FR	[56]	[83]	12	30	zb_only	50
18	Peter D. T. A. Elliott	University of Colorado Boulder	US	[56]	[83]	13	19	zb_only	57
19	R. C. Vaughan	Pennsylvania State University	US	[48]	[79]	16	35	zb_only	56
20	Yingchun Cai	Tongji University	CN	[52]	[79]	15	27	zb_only	31
21	John B. Friedlander	University of Toronto	CA	95	[90]	4	34	arx+zb	54
22	Carl Pomerance	Dartmouth College	US	80	[90]	8	39	arx+zb	54
23	Jianya Liu	Shandong University	CN	[52]	[79]	18	14	zb_only	31
24	Florian Luca	Stellenbosch University	ZA	52	173	5	28	all_three	30
25	William D. Banks	University of Missouri	US	9	98	77	21	all_three	32
26	Etienne Fouvry	Université Paris-Saclay	FR	[52]	[79]	20	28	zb_only	45
27	Jonathan Sorenson	Butler University	US	20	[92]	[49]	14	arxiv_only	35
28	Tianze Wang	Henan Academy of Sciences	CN	[52]	[79]	21	2	zb_only	35
29	Jori Merikoski	University of Helsinki	FI	8	[83]	116	2	arx+zb	5
30	Andrew Granville	Université de Montréal	CA	30	75	29	32	all_three	39
31	Lasse Grimmelt	University of Cambridge	GB	22	[92]	[49]	2	arxiv_only	7
32	Ayla Gafni	University of Mississippi	US	23	[92]	[49]	-	arxiv_only	10
33	Dieter Wolke	University of Freiburg	DE	[52]	[79]	24	-	zb_only	57
34	Jared Duker Lichtman	Stanford University	US	4	68	191	4	all_three	3
35	Valeriia Starichkova	UNSW Canberra	AU	24	[92]	[49]	2	arxiv_only	3
36	Runbo Li	University of Michigan	US	7	192	[62]	-	arx+oa	-
37	Harold G. Diamond	University of Illinois Urbana-Champaign	US	[52]	[79]	26	19	zb_only	61
38	Jörg Brüdern	University of Göttingen	DE	109	50	23	19	all_three	38
39	Yoichi Motohashi	Nihon University	JP	100	[90]	14	19	arx+zb	-
40	Henryk Iwaniec	Rutgers University	US	96	167	3	50	all_three	54
41	K. Soundararajan	Stanford University	US	17	83	95	33	all_three	28
42	András Sárközy	Eötvös Loránd University	HU	[52]	[83]	28	31	zb_only	57
43	Robert J. Lemke Oliver	Tufts University	US	28	[92]	[49]	11	arxiv_only	52
44	Imre Kátai	Eötvös Loránd University	HU	[56]	[83]	30	15	zb_only	60
45	Cem Yalçın Yıldırım	Boğaziçi University	TR	21	121	69	2	all_three	36
46	Hongze Li	Shanghai Jiao Tong University	CN	[56]	[83]	31	-	zb_only	36
47	J. P. Keating	University of Oxford	GB	32	[92]	[49]	40	arxiv_only	37
48	D. Suryanarayana	Andhra University	IN	[56]	[83]	33	20	zb_only	-
49	Roger C. Baker	Brigham Young University	US	76	[88]	27	34	arx+zb	55
50	Matt Visser	Victoria University of Wellington	NZ	35	[92]	[49]	-	arxiv_only	42
51	Jean‐Marc Deshouillers	Université de Bordeaux	FR	[48]	[83]	37	16	zb_only	54
52	Will Sawin	Princeton University	US	19	190	[59]	10	arx+oa	10
53	Damaris Schindler	University of Göttingen	DE	36	[92]	[54]	7	arxiv_only	13
54	Hugh Lowell Montgomery	University of Michigan	US	[48]	[83]	39	32	zb_only	54
55	Olivier Ramaré	Aix-Marseille Université	FR	[48]	[83]	42	15	zb_only	35
56	Zhixin Liu	Tianjin University	CN	[48]	[83]	43	-	zb_only	15
57	Ritabrata Munshi	Tata Institute of Fundamental Research	IN	29	166	[59]	12	arx+oa	20
58	Shuntaro Yamagishi	University of Bonn	DE	41	[92]	[54]	5	arxiv_only	11
59	Xuancheng Shao	University of Kentucky	US	25	[88]	137	10	arx+zb	12
60	Christian Elsholtz	Graz University of Technology	AT	[48]	[83]	45	13	zb_only	28
61	Soumyarup Banerjee	Indian Institute of Technology Bhubaneswar	IN	43	[92]	[54]	4	arxiv_only	8
62	Jean-Louis Nicolas	University of Lyon	FR	[48]	[83]	46	16	zb_only	57
63	Angel Kumchev	Towson University	US	81	[90]	36	12	arx+zb	25
64	Adolf Hildebrand	University of Illinois Urbana-Champaign	US	[48]	[83]	47	19	zb_only	43
65	Cameron L. Stewart	University of Waterloo	CA	[48]	[83]	48	20	zb_only	50
66	David Lowry-Duda	Brown University	US	46	[92]	[54]	5	arxiv_only	9
67	Richard A. Mollin	University of Calgary	CA	[52]	[83]	50	18	zb_only	51
68	Alexandru Zaharescu	University of Illinois Urbana-Champaign	US	[20]	70	[40]	24	oa_only	35
69	Jiseong Kim	University of Mississippi	US	50	[98]	[62]	20	arxiv_only	3
70	Tao Zhan	Shandong University	CN	[52]	[83]	55	17	zb_only	39
71	H. A. Helfgott	Université Paris Cité	FR	44	[88]	91	19	arx+zb	23
72	Felix Sidokhine	Independent	CA	51	[98]	[62]	-	arxiv_only	-
73	Antal Balog	Alfréd Rényi Institute of Mathematics	HU	[52]	[83]	56	18	zb_only	35
74	Alex Kontorovich	Rutgers University	US	40	[84]	134	13	arx+zb	19
75	George Greaves	University of Wales	GB	[52]	[83]	57	11	zb_only	-
76	Ofir Gorodetsky	Technion - Israel Institute of Technology	IL	53	[98]	[69]	5	arxiv_only	5
77	H. J. Weber	University of Virginia	US	54	[98]	[69]	-	arxiv_only	61
78	Kai-Man Tsang	University of Hong Kong	HK	[52]	[83]	61	8	zb_only	42
79	Yong-Gao Chen	Nanjing Normal University	CN	[52]	[83]	62	-	zb_only	34
80	Nicolas Robles	RAND Corporation	US	49	172	[55]	7	arx+oa	11
81	Apoorva Panidapu	Massachusetts Institute of Technology	US	55	[98]	[72]	-	arxiv_only	-
82	Jean-Marie De Koninck	Université Laval	CA	[52]	[83]	63	10	zb_only	53
83	Fred B. Holt	Independent	US	45	[88]	140	6	arx+zb	30
84	Doychin Tolev	Sofia University "St. Kliment Ohridski"	BG	115	[106]	44	10	arx+zb	25
85	V. N. Chubarikov	Lomonosov Moscow State University	RU	[52]	[83]	64	-	zb_only	49
86	Tristan Freiberg	University of Waterloo	CA	38	[88]	199	4	arx+zb	16
87	S. I. Dimitrov	Technical University of Sofia	BG	[52]	[83]	65	6	zb_only	-
88	Huafeng Liu	Shandong Normal University	CN	[52]	[83]	66	55	zb_only	9
89	Paweł Lewulis	University of Warsaw	PL	58	[110]	[72]	1	arxiv_only	-
90	Enrico Bombieri	Institute for Advanced Study	US	[52]	[83]	68	42	zb_only	63
91	V. A. Plaksin	Petrozavodsk State University	RU	[56]	[83]	71	3	zb_only	-
92	Claus Bauer	Dolby Laboratories	US	[56]	[83]	72	7	zb_only	30
93	Michael Th. Rassias	Hellenic Military Academy	GR	66	124	[58]	24	arx+oa	12
94	M. Ram Murty	Queen's University	CA	[29]	87	[40]	25	oa_only	46
95	Stephan Ramon Garcia	Pomona College	US	68	[98]	[72]	27	arxiv_only	23
96	Liangyi Zhao	UNSW Sydney	AU	[56]	[83]	75	14	zb_only	37
97	Helmut Maier	Universität Ulm	DE	165	[108]	49	18	arx+zb	45
98	Régis de la Bretèche	Université Paris Cité	FR	70	[98]	[70]	14	arxiv_only	30
99	Xianmeng Meng	Shandong University of Finance and Economics	CN	[59]	[83]	76	7	zb_only	-
100	Olli Järviniemi	University of Turku	FI	71	[98]	[70]	3	arxiv_only	3

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
`zb_only`	37
`arxiv_only`	20
`all_three`	17
`arx+zb`	16
`arx+oa`	6
`oa_only`	4

Limitations

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