The Top 100

Researchers active on Goldbach, Legendre's conjecture, n2+1 primes, twin 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
gb rank on the Goldbach list (dash: not on that list)
leg rank on the Legendre's conjecture list (dash: not on that list)
n2p1 rank on the n2+1 primes list (dash: not on that list)
tp rank on the twin primes list (dash: not on that list)
h h-index (citation impact)
Source which member problems 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. This list is a consolidation of the four member directories (Goldbach, Legendre's conjecture, n2+1 primes and twin primes). Each member list ranks a researcher on that one problem; those ranks are fused into one umbrella rank, so a researcher strong on several of the four finishes ahead of a researcher equally strong on only one. A dash means the researcher is not on that member list. Lower is better. Click any header to sort. Full method.

#	Name	Institution		gb	leg	n2p1	tp	h	Source	YSP
1	Janos Pintz	Alfréd Rényi Institute of Mathematics	HU	3	2	12	1	26	gb+leg+n2p1+tp	50
2	Henryk Iwaniec	Rutgers University	US	8	13	1	3	50	gb+leg+n2p1+tp	54
3	D. R. Heath-Brown	University of Oxford	GB	5	4	4	17	45	gb+leg+n2p1+tp	47
4	Glyn Harman	Royal Holloway University of London	GB	10	3	5	20	19	gb+leg+n2p1+tp	44
5	John B. Friedlander	University of Toronto	CA	23	8	2	7	34	gb+leg+n2p1+tp	54
6	Terence Tao	University of California, Los Angeles	US	7	5	29	4	101	gb+leg+n2p1+tp	30
7	Kaisa Matomäki	University of Turku	FI	26	1	24	8	16	gb+leg+n2p1+tp	17
8	Daniel A. Goldston	San Jose State University	US	12	6	-	2	21	gb+leg+tp	45
9	R. C. Vaughan	Pennsylvania State University	US	1	-	20	14	35	gb+n2p1+tp	56
10	Etienne Fouvry	University of Paris-Saclay	FR	37	17	9	10	28	gb+leg+n2p1+tp	45
11	James Maynard	University of Oxford	GB	40	12	22	6	11	gb+leg+n2p1+tp	13
12	Carl Pomerance	Dartmouth College	US	51	19	11	18	39	gb+leg+n2p1+tp	54
13	Andrew Granville	Université de Montréal	CA	15	27	26	13	32	gb+leg+n2p1+tp	39
14	M. Ram Murty	Queen's University	CA	54	-	3	16	25	gb+n2p1+tp	46
15	Trevor D. Wooley	Purdue University West Lafayette	US	2	80	61	-	28	gb+leg+n2p1+tp	36
16	Jörg Brüdern	University of Göttingen	DE	4	35	35	72	19	gb+leg+n2p1+tp	38
17	Hugh Lowell Montgomery	University of Michigan	US	11	57	39	11	32	gb+leg+n2p1+tp	54
18	Jie Wu	Université Paris-Est Créteil Val-de-Marne	FR	34	14	16	29	19	gb+leg+n2p1+tp	36
19	Runbo Li	The High School Affiliated to Renmin University of China	CN	84	9	15	57	-	gb+leg+n2p1+tp	-
20	Joni Teräväinen	University of Cambridge	GB	44	11	18	42	9	gb+leg+n2p1+tp	8
21	K. Soundararajan	Stanford University	US	68	15	54	15	33	gb+leg+n2p1+tp	28
22	Paul Pollack	University of Georgia	US	-	22	13	25	13	gb+leg+n2p1+tp	18
23	Yoichi Motohashi	Nihon University	JP	-	61	8	23	19	leg+n2p1+tp	-
24	Stephan Baier	Ramakrishna Mission Vivekananda Educational and Research Institute	IN	-	32	6	62	14	leg+n2p1+tp	26
25	Angel Kumchev	Towson University	US	9	50	36	85	12	gb+leg+n2p1+tp	25
26	Alessandro Zaccagnini	University of Parma	IT	21	7	-	-	14	gb+leg+tp	32
27	Emmanuel Kowalski	ETH Zurich	CH	39	53	32	21	29	gb+leg+n2p1+tp	28
28	Peter D. T. A. Elliott	University of Colorado Boulder	US	100	-	14	19	19	gb+n2p1+tp	57
29	Alessandro Languasco	University of Padua	IT	19	10	-	-	12	gb+leg+tp	30
30	Roger C. Baker	Brigham Young University	US	13	25	-	31	23	gb+leg+tp	55
31	Kevin Ford	University of Illinois Urbana-Champaign	US	83	26	25	32	-	gb+leg+n2p1+tp	32
32	Yitang Zhang	University of California, Santa Barbara	US	60	-	-	5	-	gb+tp	35
33	Alberto Perelli	University of Genoa	IT	27	28	62	38	20	gb+leg+n2p1+tp	50
34	Igor E. Shparlinski	University of New South Wales	AU	36	-	7	-	42	gb+n2p1	46
35	Cem Yalçın Yıldırım	Boğaziçi University	TR	95	52	-	9	2	gb+leg+tp	36
36	Enrico Bombieri	Institute for Advanced Study	US	22	-	-	12	42	gb+tp	63
37	Jianya Liu	Shandong University	CN	6	65	-	-	19	gb+leg	31
38	Gérald Tenenbaum	Institut Élie Cartan de Lorraine	FR	86	-	19	24	30	gb+n2p1+tp	50
39	William D. Banks	University of Missouri	US	76	56	44	26	21	gb+leg+n2p1+tp	32
40	Chaohua Jia	Chinese Academy of Sciences	CN	38	23	-	66	11	gb+leg+tp	39
41	Antal Balog	Alfréd Rényi Institute of Mathematics	HU	41	66	45	63	18	gb+leg+n2p1+tp	35
42	Hongze Li	Shanghai Jiao Tong University	CN	14	55	-	64	-	gb+leg+tp	36
43	Harold G. Diamond	University of Illinois Urbana-Champaign	US	-	31	28	-	19	leg+n2p1+tp	61
44	S. W. Graham	Central Michigan University	US	77	78	53	27	15	gb+leg+n2p1+tp	49
45	Ben Green	University of Oxford	GB	20	87	-	30	5	gb+leg+tp	23
46	Jean‐Marc Deshouillers	University of Bordeaux	FR	35	-	30	50	16	gb+n2p1+tp	54
47	Jesse Thorner	University of Illinois Urbana-Champaign	US	-	20	84	61	9	leg+n2p1+tp	10
48	Hao Pan	Nanjing University of Finance and Economics	CN	63	62	41	65	17	gb+leg+n2p1+tp	20
49	Efthymios Sofos	University of Rome Tor Vergata	IT	-	-	10	-	7	n2p1	11
50	Sergey Konyagin	Steklov Mathematical Institute	RU	-	40	40	56	28	leg+n2p1+tp	44
51	Jori Merikoski	University of Helsinki	FI	89	46	57	75	2	gb+leg+n2p1+tp	5
52	Wenguang Zhai	China University of Mining and Technology (Beijing)	CN	57	37	55	-	13	gb+leg+n2p1	30
53	Doychin Tolev	Sofia University	BG	30	-	38	81	10	gb+n2p1+tp	25
54	Ofir Gorodetsky	Technion - Israel Institute of Technology	IL	-	16	-	-	5	leg+tp	5
55	M. N. Huxley	Cardiff University	GB	33	76	-	48	23	gb+leg+tp	56
56	Alexandru Zaharescu	University of Illinois Urbana-Champaign	US	73	42	59	-	24	gb+leg+n2p1	35
57	Cameron L. Stewart	University of Waterloo	CA	-	41	50	-	20	gb+leg+n2p1	50
58	Koichi Kawada	Iwate University	JP	18	-	64	-	9	gb+n2p1	32
59	Xuancheng Shao	University of Kentucky	US	43	47	-	77	10	gb+leg+tp	12
60	Brad Rodgers	Queen's University	CA	-	18	-	-	8	leg+tp	13
61	Guangshi Lü	Shandong University	CN	28	43	-	-	17	gb+leg	22
62	Jiseong Kim	University of Mississippi	US	-	21	-	-	1	gb+leg	3
63	Yu-Chen Sun	University of Turku	FI	-	24	-	67	-	leg+tp	-
64	Helmut Maier	University of Ulm	DE	-	51	-	35	18	gb+leg+tp	45
65	András Sárközy	Eötvös Loránd University	HU	58	-	27	-	31	gb+n2p1	57
66	Adolf Hildebrand	University of Illinois Urbana-Champaign	US	96	44	-	53	19	gb+leg+tp	43
67	Alexander K. Zvonkin	University of Bordeaux	FR	-	-	17	-	12	n2p1	53
68	Stephan Ramon Garcia	Pomona College	US	-	-	23	80	27	n2p1+tp	23
69	Peter Sarnak	Princeton University	US	-	-	21	-	57	n2p1+tp	46
70	Tristan Freiberg	University of Waterloo	CA	-	34	-	52	4	leg+tp	16
71	Timothy S. Trudgian	UNSW Canberra	AU	71	79	76	-	13	gb+leg+n2p1	16
72	Imre Z. Ruzsa	Alfréd Rényi Institute of Mathematics	HU	49	-	70	-	33	gb+n2p1+tp	47
73	Lilu Zhao	University of Science and Technology of China	CN	32	-	67	-	10	gb+n2p1	23
74	H. A. Helfgott	Université Paris Cité	FR	46	-	48	-	19	gb+n2p1	23
75	Adrian Dudek	University of Queensland	AU	-	29	-	-	5	leg+tp	10
76	Philippe Michel	École Polytechnique Fédérale de Lausanne	CH	-	-	33	73	-	n2p1+tp	31
77	Régis de la Bretèche	Université Paris Cité	FR	-	77	73	-	14	leg+n2p1+tp	30
78	Mayank Pandey	Princeton University	US	-	33	-	-	-	gb+leg	-
79	Jinjiang Li	China University of Mining and Technology (Beijing)	CN	16	-	-	-	6	gb	-
80	Tao Zhan	Shandong University	CN	17	-	-	-	16	gb	39
81	Melvyn B. Nathanson	Lehman College, CUNY	US	55	-	-	33	-	gb+tp	54
82	S. Salerno	University of Salerno	IT	-	71	51	-	-	leg+n2p1	-
83	Imre Kátai	Eötvös Loránd University	HU	-	-	34	-	15	gb+n2p1	60
84	Lasse Grimmelt	University of Cambridge	GB	72	-	88	87	2	gb+n2p1+tp	7
85	Roger A. Horn	University of Utah	US	-	-	-	22	29	tp	59
86	Jerzy Kaczorowski	Adam Mickiewicz University in Poznań	PL	-	39	-	-	19	gb+leg	43
87	Sun-Kai Leung	University of Oxford	GB	-	38	-	-	1	leg+tp	1
88	Olivier Ramaré	Aix-Marseille University	FR	56	-	-	46	15	gb+tp	35
89	Efrat Bank	Tel Aviv University	IL	-	30	-	-	3	leg	11
90	Michael Th. Rassias	Hellenic Military Academy	GR	-	63	-	-	24	gb+leg+tp	12
91	J. P. Keating	University of Oxford	GB	-	58	-	68	40	leg+tp	37
92	Karin Halupczok	Heinrich Heine University Düsseldorf	DE	61	-	66	-	5	gb+n2p1	25
93	H. J. J. te Riele	Centrum Wiskunde & Informatica	NL	62	-	-	47	-	gb+tp	50
94	Liangyi Zhao	University of New South Wales	AU	-	-	31	-	14	n2p1	23
95	Tianze Wang	Henan Academy of Sciences	CN	24	-	-	-	2	gb	35
96	Alex Kontorovich	Rutgers University	US	-	-	49	-	13	n2p1+tp	19
97	Zeev Rudnick	Tel Aviv University	IL	-	49	-	-	32	leg+tp	36
98	Hugh C. Williams	University of Calgary	CA	-	-	46	-	18	n2p1+tp	57
99	Greg Martin	University of British Columbia	CA	-	85	68	-	16	leg+n2p1	29
100	Vivian Kuperberg	ETH Zurich	CH	-	48	-	-	3	leg+tp	4

Source column legend

The Source column records which of the four member problem directories list each researcher. The umbrella rank is a fusion of the member ranks, so a researcher on several lists gains ground on a researcher of similar standing on only one.

gb: ranked on the Goldbach list (wwigb.org)
leg: ranked on the Legendre's conjecture list (wwileg.org)
n2p1: ranked on the n2+1 primes list (wwin2p1.org)
tp: ranked on the twin primes list (wwitp.org)
codes are joined with + when a researcher appears on more than one member list, in the order gb leg n2p1 tp

Source	Count
`gb+leg+n2p1+tp`	28
`gb+leg+tp`	13
`leg+tp`	9
`gb+n2p1+tp`	8
`gb+n2p1`	7
`leg+n2p1+tp`	6
`gb+tp`	5
`gb+leg`	5
`n2p1+tp`	5
`gb+leg+n2p1`	4
`n2p1`	3
`gb`	3
`leg+n2p1`	2
`tp`	1
`leg`	1

Limitations

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