The Top 100

Researchers active on the twin prime conjecture, bounded gaps between primes, and prime pair sieve theory

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
Cit citation-influence rank: how many works in the literature on this conjecture cite them, by reference or by name
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 rank a researcher by their own papers, and the Cit column ranks how often the literature cites them ; the score is the geometric mean of the Cit rank and the combined paper rank, so a researcher needs both to rank high. Researchers with work on the problem, or cited by work on it, are listed first. 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	Cit	h	Source	YSP
1	Janos Pintz	Alfréd Rényi Institute of Mathematics	HU	3	6	2	5	26	all_three	50
2	Daniel A. Goldston	San Jose State University	US	8	12	9	6	21	all_three	45
3	Henryk Iwaniec	Rutgers University	US	[43]	129	3	4	50	oa+zb	54
4	Terence Tao	University of California, Los Angeles	US	4	18	39	12	101	all_three	30
5	Yitang Zhang	University of California, Santa Barbara	US	[51]	[54]	[38]	3	-	cite_only	35
6	James Maynard	University of Oxford	GB	16	81	21	7	11	all_three	13
7	John B. Friedlander	University of Toronto	CA	72	59	4	8	34	all_three	54
8	Kaisa Matomäki	University of Turku	FI	1	8	33	53	16	all_three	17
9	Cem Yalçın Yıldırım	Boğaziçi University	TR	33	84	50	9	2	all_three	36
10	Etienne Fouvry	University of Paris-Saclay	FR	[38]	[57]	17	19	28	zb_only	45
11	Hugh Lowell Montgomery	University of Michigan	US	[40]	[57]	34	13	32	zb_only	54
12	Enrico Bombieri	Institute for Advanced Study	US	[40]	[57]	51	11	42	zb_only	63
13	Andrew Granville	Université de Montréal	CA	71	52	27	15	32	all_three	39
14	R. C. Vaughan	Pennsylvania State University	US	[40]	[56]	37	14	35	zb_only	56
15	K. Soundararajan	Stanford University	US	11	46	77	23	33	all_three	28
16	M. Ram Murty	Queen's University	CA	[37]	94	11	28	25	oa+zb	46
17	D. R. Heath-Brown	University of Oxford	GB	91	48	6	34	45	all_three	47
18	Carl Pomerance	Dartmouth College	US	79	83	8	30	39	all_three	54
19	Peter D. T. A. Elliott	University of Colorado Boulder	US	[35]	[60]	14	40	19	zb_only	57
20	Glyn Harman	Royal Holloway University of London	GB	[34]	64	7	58	19	oa+zb	44
21	Emmanuel Kowalski	ETH Zurich	CH	[35]	[58]	53	24	29	zb_only	28
22	Roger A. Horn	University of Utah	US	[42]	[56]	[40]	32	29	cite_only	59
23	Yoichi Motohashi	Nihon University	JP	82	[68]	15	42	19	arx+zb	-
24	Gérald Tenenbaum	Institut Élie Cartan de Lorraine	FR	[36]	[60]	13	62	30	zb_only	50
25	Paul Pollack	University of Georgia	US	19	47	32	60	13	all_three	18
26	William D. Banks	University of Missouri	US	13	32	70	81	21	all_three	32
27	S. W. Graham	Central Michigan University	US	[37]	[59]	84	27	15	zb_only	49
28	Richard P. Brent	Australian National University	AU	[40]	[60]	[47]	45	45	cite_only	55
29	Jie Wu	Université Paris-Est Créteil Val-de-Marne	FR	50	23	24	84	19	all_three	36
30	Ben Green	University of Oxford	GB	104	[79]	157	21	5	arx+zb	23
31	Roger C. Baker	Brigham Young University	US	120	104	19	52	23	all_three	55
32	Kevin Ford	University of Illinois Urbana-Champaign	US	18	[68]	31	105	-	arx+zb	32
33	Melvyn B. Nathanson	Lehman College, CUNY	US	[40]	[60]	[46]	64	-	cite_only	54
34	Michael Rosen	Brown University	US	[40]	[60]	[47]	68	19	cite_only	63
35	Helmut Maier	University of Ulm	DE	101	85	47	50	18	all_three	45
36	Wouter Castryck	KU Leuven	BE	[40]	[60]	[47]	70	19	cite_only	20
37	Gergely Harcos	Alfréd Rényi Institute of Mathematics	HU	[38]	[61]	[47]	73	14	cite_only	23
38	Alberto Perelli	University of Genoa	IT	[32]	54	41	78	20	oa+zb	50
39	Paul D. Nelson	Aarhus University	DK	[38]	[61]	[47]	76	11	cite_only	15
40	Paulo Ribenboim	Queen's University	CA	[38]	[76]	156	26	29	zb_only	69
41	Eytan Paldi	-	-	[38]	[61]	[47]	77	3	cite_only	-
42	Joni Teräväinen	University of Cambridge	GB	2	19	113	[200]	9	all_three	8
43	Andrew V. Sutherland	Massachusetts Institute of Technology	US	[38]	[61]	[47]	79	19	cite_only	19
44	Paul A. Clement	-	-	[38]	[61]	[47]	82	-	cite_only	77
45	Pierre Dusart	Université de Limoges	FR	[38]	[61]	[48]	86	10	cite_only	28
46	Olivier Ramaré	Aix-Marseille University	FR	[36]	[61]	28	113	15	zb_only	35
47	H. J. J. te Riele	Centrum Wiskunde & Informatica	NL	[38]	[61]	[48]	88	-	cite_only	50
48	M. N. Huxley	Cardiff University	GB	[37]	[61]	76	56	23	zb_only	56
49	Joseph H. Silverman	Brown University	US	[38]	[61]	[48]	90	56	cite_only	44
50	Jean‐Marc Deshouillers	University of Bordeaux	FR	[32]	[61]	45	94	16	zb_only	54
51	William D. Duke	University of California, Los Angeles	US	[36]	[61]	[50]	104	28	cite_only	40
52	Tristan Freiberg	University of Waterloo	CA	20	60	100	120	4	all_three	16
53	Adolf Hildebrand	University of Illinois Urbana-Champaign	US	[36]	[61]	40	108	19	zb_only	43
54	Chris Hall	Western University	CA	[38]	[61]	[50]	106	10	cite_only	23
55	Robert J. Lemke Oliver	University of Wisconsin-Madison	US	54	189	[73]	65	11	arx+oa	13
56	Sergey Konyagin	Steklov Mathematical Institute	RU	26	61	60	134	28	all_three	44
57	Runbo Li	The High School Affiliated to Renmin University of China	CN	17	35	[62]	[200]	-	arx+oa	-
58	Donald E. Knuth	Stanford University	US	[40]	[63]	[60]	123	83	cite_only	63
59	Bernard Host	Université Gustave Eiffel	FR	[42]	[63]	[60]	121	29	cite_only	47
60	Henry J. Ricardo	Medgar Evers College	US	[42]	[64]	[58]	127	7	cite_only	54
61	Jesse Thorner	University of Illinois Urbana-Champaign	US	42	98	[65]	116	9	arx+oa	10
62	Stephan Baier	Ramakrishna Mission Vivekananda Educational and Research Institute	IN	44	141	12	[200]	14	all_three	26
63	Antal Balog	Alfréd Rényi Institute of Mathematics	HU	105	187	61	85	18	all_three	35
64	Hongze Li	Shanghai Jiao Tong University	CN	[33]	[62]	56	137	-	zb_only	36
65	Hao Pan	Nanjing University of Finance and Economics	CN	38	121	71	140	17	all_three	20
66	Chaohua Jia	Chinese Academy of Sciences	CN	[30]	[61]	36	[200]	11	zb_only	39
67	Yu-Chen Sun	University of Turku	FI	22	[84]	[70]	[200]	-	arxiv_only	-
68	J. P. Keating	University of Oxford	GB	28	[73]	[66]	[200]	40	arxiv_only	37
69	Lynn Chua	Google	US	[27]	[80]	[71]	[200]	-	cite_only	6
70	Lior Bary-Soroker	Tel Aviv University	IL	34	58	[61]	[200]	10	arx+oa	18
71	Abel Castillo	-	-	[34]	[63]	[61]	[200]	3	cite_only	-
72	Jörg Brüdern	University of Göttingen	DE	[28]	[71]	46	[200]	19	zb_only	38
73	Philippe Michel	École Polytechnique Fédérale de Lausanne	CH	[48]	[78]	195	59	-	zb_only	31
74	Frieder Grupp	University of Ulm	DE	[34]	[78]	163	72	-	zb_only	46
75	Jori Merikoski	University of Helsinki	FI	24	96	112	[200]	2	all_three	5
76	Fred B. Holt	Independent	US	29	97	93	[200]	6	all_three	30
77	Xuancheng Shao	University of Kentucky	US	23	125	139	[200]	10	all_three	12
78	Valeriia Starichkova	UNSW Canberra	AU	48	[84]	[70]	[200]	2	arxiv_only	3
79	Alina Carmen Cojocaru	University of Illinois Chicago	US	[28]	[70]	62	[200]	14	zb_only	24
80	Stephan Ramon Garcia	Pomona College	US	43	126	[69]	[200]	27	arx+oa	23
81	Doychin Tolev	Sofia University	BG	[30]	[61]	68	[200]	10	zb_only	25
82	Kevin Broughan	University of Waikato	NZ	[35]	50	179	[200]	12	oa+zb	51
83	Will Sawin	Princeton University	US	40	173	[76]	[200]	10	arx+oa	10
84	Lola Thompson	Utrecht University	NL	93	[73]	[66]	143	-	arxiv_only	14
85	Angel Kumchev	Towson University	US	92	[72]	57	[200]	12	arx+zb	25
86	Douglas Azevedo	Universidade Tecnologica Federal do Parana	BR	64	[84]	[70]	[200]	5	arxiv_only	13
87	Lasse Grimmelt	University of Cambridge	GB	65	[84]	[70]	[200]	2	arxiv_only	7
88	David Lowry-Duda	Brown University	US	59	139	[68]	[200]	5	arx+oa	9
89	H. J. Weber	University of Virginia	US	55	[90]	170	[200]	-	arx+zb	61
90	Hiroshi Mikawa	University of Tsukuba	JP	[36]	[76]	143	138	-	zb_only	36
91	Akshaa Vatwani	Indian Institute of Technology Gandhinagar	IN	[35]	134	129	144	6	oa+zb	10
92	A. H. Ledoan	University of Tennessee at Chattanooga	US	56	119	186	[200]	-	all_three	19
93	Chantal David	Concordia University	CA	87	[84]	[70]	[200]	14	arxiv_only	33
94	Maurizio Laporta	University of Naples Federico II	IT	77	166	[76]	[200]	5	arx+oa	-
95	Jacques Benatar	-	BE	95	[84]	[70]	[200]	3	arxiv_only	11
96	Karl-Heinz Indlekofer	Paderborn University	DE	[31]	[71]	114	[200]	10	zb_only	56
97	Jared Duker Lichtman	Stanford University	US	85	[90]	161	[200]	4	arx+zb	3
98	Minggao Lu	Shanghai University	CN	[29]	[71]	119	[200]	3	zb_only	-
99	Dale J. Smith	University of Bristol	GB	107	[95]	[74]	[200]	-	arxiv_only	-
100	Tamar Ziegler	Hebrew University of Jerusalem	IL	[32]	[80]	174	147	14	zb_only	23

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.
cite_only: ranked only by citation influence: the literature cites them heavily, though they have written few papers on the topic themselves. Often the founders of the field.

Source	Count
`all_three`	26
`zb_only`	24
`cite_only`	21
`arxiv_only`	9
`arx+oa`	8
`oa+zb`	6
`arx+zb`	6

Limitations

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