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	-	1	26	gb+leg+tp	50
2	Kaisa Matomäki	University of Turku	FI	11	1	22	2	16	gb+leg+n2p1+tp	17
3	Terence Tao	University of California, Los Angeles	US	6	3	30	4	101	gb+leg+n2p1+tp	30
4	D. R. Heath-Brown	University of Oxford	GB	14	4	3	12	45	gb+leg+n2p1+tp	47
5	Daniel A. Goldston	San Jose State University	US	4	5	-	3	21	gb+leg+tp	45
6	Henryk Iwaniec	Rutgers University	US	71	16	1	5	50	gb+leg+n2p1+tp	54
7	Glyn Harman	Royal Holloway University of London	GB	19	6	5	16	19	gb+leg+n2p1+tp	44
8	John B. Friedlander	University of Toronto	CA	79	7	2	8	34	gb+leg+n2p1+tp	54
9	Joni Teräväinen	University of Cambridge	GB	8	17	26	6	9	gb+leg+n2p1+tp	8
10	Stephan Baier	Ramakrishna Mission Vivekananda Educational and Research Institute	IN	17	29	6	22	14	gb+leg+n2p1+tp	26
11	Runbo Li	The High School Affiliated to Renmin University of China	CN	42	9	15	11	-	gb+leg+n2p1+tp	-
12	Carl Pomerance	Dartmouth College	US	44	11	11	25	39	gb+leg+n2p1+tp	54
13	Paul Pollack	University of Georgia	US	80	18	12	10	13	gb+leg+n2p1+tp	18
14	Alessandro Languasco	University of Padua	IT	16	10	-	9	12	gb+leg+tp	30
15	Trevor D. Wooley	Purdue University West Lafayette	US	1	73	58	99	28	gb+leg+n2p1+tp	36
16	James Maynard	University of Oxford	GB	40	12	20	14	11	gb+leg+n2p1+tp	13
17	Etienne Fouvry	Université Paris-Saclay	FR	77	21	10	17	28	gb+leg+n2p1+tp	45
18	Alessandro Zaccagnini	University of Parma	IT	18	8	-	19	14	gb+leg+tp	32
19	Igor E. Shparlinski	UNSW Sydney	AU	7	-	7	-	42	gb+n2p1	46
20	Jörg Brüdern	University of Göttingen	DE	9	34	35	39	19	gb+leg+n2p1+tp	38
21	M. Ram Murty	Queen's University	CA	33	-	4	23	25	gb+n2p1+tp	46
22	Andrew Granville	Université de Montréal	CA	28	28	13	34	32	gb+leg+n2p1+tp	39
23	Kevin Ford	University of Illinois Urbana-Champaign	US	38	22	23	18	-	gb+leg+n2p1+tp	32
24	Jie Wu	Université Paris-Est Créteil Val-de-Marne	FR	54	19	16	27	19	gb+leg+n2p1+tp	36
25	K. Soundararajan	Stanford University	US	-	13	52	7	33	leg+n2p1+tp	28
26	William D. Banks	University of Missouri	US	41	40	41	13	21	gb+leg+n2p1+tp	32
27	Yoichi Motohashi	Nihon University	JP	-	67	9	26	19	gb+leg+n2p1+tp	-
28	Jinjiang Li	China University of Mining and Technology (Beijing)	CN	2	-	-	-	6	gb	-
29	Harold G. Diamond	University of Illinois Urbana-Champaign	US	-	32	27	15	19	leg+n2p1+tp	61
30	R. C. Vaughan	Pennsylvania State University	US	10	-	19	-	35	gb+n2p1	56
31	Alberto Perelli	University of Genoa	IT	37	31	59	37	20	gb+leg+n2p1+tp	50
32	Angel Kumchev	Towson University	US	31	44	33	64	12	gb+leg+n2p1+tp	25
33	Efthymios Sofos	University of Rome Tor Vergata	IT	92	89	8	-	7	gb+leg+n2p1	11
34	Roger C. Baker	Brigham Young University	US	26	26	-	48	34	gb+leg+tp	55
35	Min Zhang	Beijing Information Science and Technology University	CN	5	-	-	-	44	gb	-
36	Ofir Gorodetsky	Technion - Israel Institute of Technology	IL	-	14	-	20	5	leg+tp	5
37	Jesse Thorner	University of Illinois Urbana-Champaign	US	60	25	81	43	9	gb+leg+n2p1+tp	10
38	Xuancheng Shao	University of Kentucky	US	22	37	-	51	10	gb+leg+tp	12
39	Jori Merikoski	University of Helsinki	FI	48	45	55	41	2	gb+leg+n2p1+tp	5
40	Jianya Liu	Shandong University	CN	15	63	-	70	14	gb+leg+tp	31
41	Hugh Lowell Montgomery	University of Michigan	US	-	53	36	31	32	gb+leg+n2p1+tp	54
42	Chaohua Jia	Chinese Academy of Sciences	CN	34	35	-	33	11	gb+leg+tp	39
43	Hongze Li	Shanghai Jiao Tong University	CN	20	55	-	57	-	gb+leg+tp	36
44	Emmanuel Kowalski	ETH Zurich	CH	100	61	31	44	29	gb+leg+n2p1+tp	28
45	Brad Rodgers	Queen's University	CA	-	15	-	28	8	leg+tp	13
46	Hao Pan	Nanjing University of Finance and Economics	CN	62	68	38	46	17	gb+leg+n2p1+tp	20
47	Alexandru Zaharescu	University of Illinois Urbana-Champaign	US	46	43	66	93	24	gb+leg+n2p1+tp	35
48	Doychin Tolev	Sofia University "St. Kliment Ohridski"	BG	36	-	34	60	10	gb+n2p1+tp	25
49	Adrian Dudek	University of Queensland	AU	57	30	-	47	5	gb+leg+tp	10
50	Yu-Chen Sun	University of Turku	FI	-	20	-	30	-	leg+tp	-
51	András Sárközy	Eötvös Loránd University	HU	25	-	24	-	31	gb+n2p1	57
52	Antal Balog	Alfréd Rényi Institute of Mathematics	HU	72	66	42	68	18	gb+leg+n2p1+tp	35
53	Peter D. T. A. Elliott	University of Colorado Boulder	US	64	-	14	-	19	gb+n2p1	57
54	Vivian Kuperberg	ETH Zurich	CH	-	36	-	21	3	leg+tp	4
55	Tianze Wang	Henan Academy of Sciences	CN	12	-	-	-	2	gb	35
56	Stephan Ramon Garcia	Pomona College	US	-	-	21	42	27	n2p1+tp	23
57	Guangshi Lü	Shandong University	CN	23	50	-	-	17	gb+leg	22
58	Wenguang Zhai	China University of Mining and Technology (Beijing)	CN	45	54	53	-	13	gb+leg+n2p1	30
59	Jean‐Marc Deshouillers	Université de Bordeaux	FR	32	-	28	-	16	gb+n2p1	54
60	Yingchun Cai	Tongji University	CN	13	-	-	-	27	gb	31
61	Koichi Kawada	Iwate University	JP	21	-	61	-	9	gb+n2p1	32
62	Cameron L. Stewart	University of Waterloo	CA	82	42	47	-	20	gb+leg+n2p1	50
63	Cem Yalçın Yıldırım	Boğaziçi University	TR	-	58	-	32	2	gb+leg+tp	36
64	Michael Th. Rassias	Hellenic Military Academy	GR	94	52	-	40	24	gb+leg+tp	12
65	Timothy S. Trudgian	UNSW Canberra	AU	85	79	74	83	13	gb+leg+n2p1+tp	16
66	Jiseong Kim	University of Mississippi	US	65	24	-	-	20	gb+leg	3
67	Helmut Maier	Universität Ulm	DE	93	48	-	56	18	gb+leg+tp	45
68	Lasse Grimmelt	University of Cambridge	GB	47	-	85	63	2	gb+n2p1+tp	7
69	Jared Duker Lichtman	Stanford University	US	24	-	-	84	4	gb+tp	3
70	Sergey Konyagin	Steklov Mathematical Institute	RU	-	41	37	-	28	leg+n2p1	44
71	S. W. Graham	Central Michigan University	US	-	78	51	72	15	leg+n2p1+tp	49
72	Adolf Hildebrand	University of Illinois Urbana-Champaign	US	-	46	-	36	19	leg+tp	43
73	Greg Martin	University of British Columbia	CA	-	83	65	-	16	gb+leg+n2p1+tp	29
74	Olivier Ramaré	Aix-Marseille Université	FR	68	-	-	29	15	gb+tp	35
75	Alexander K. Zvonkin	Université de Bordeaux	FR	-	-	17	-	12	n2p1	53
76	Giovanni Coppola	University of Salerno	IT	-	-	-	24	6	gb+tp	-
77	Ben Green	University of Oxford	GB	53	85	-	96	5	gb+leg+tp	23
78	Régis de la Bretèche	Université Paris Cité	FR	-	74	71	86	14	leg+n2p1+tp	30
79	Gérald Tenenbaum	Institut Élie Cartan de Lorraine	FR	-	-	18	-	30	n2p1	50
80	Imre Kátai	Eötvös Loránd University	HU	84	-	32	-	15	gb+n2p1	60
81	J. P. Keating	University of Oxford	GB	-	51	-	52	40	leg+tp	37
82	Minggao Lu	Shanghai University	CN	90	84	-	89	3	gb+leg+tp	-
83	Matt Visser	Victoria University of Wellington	NZ	-	23	-	-	-	leg	42
84	Tristan Freiberg	University of Waterloo	CA	-	62	-	54	4	leg+tp	16
85	D. Bazzanella	Politecnico di Torino	IT	-	57	-	59	-	leg+tp	30
86	Will Sawin	Princeton University	US	59	-	-	53	10	gb+tp	10
87	Karin Halupczok	Heinrich Heine University Düsseldorf	DE	49	-	63	-	5	gb+n2p1	25
88	S. Salerno	University of Salerno	IT	-	69	48	-	-	leg+n2p1	-
89	Fred B. Holt	Independent	US	-	72	-	49	6	leg+tp	30
90	Aled Walker	Kings College London	GB	-	77	-	81	-	gb+leg+tp	8
91	H. A. Helfgott	Université Paris Cité	FR	87	-	45	-	19	gb+n2p1	23
92	Efrat Bank	Tel Aviv University	IL	-	27	-	-	3	leg	11
93	Zhixin Liu	Tianjin University	CN	27	-	-	-	-	gb	15
94	Edva Roditty-Gershon	University of Bristol	GB	-	56	-	75	-	leg+tp	11
95	Alex Kontorovich	Rutgers University	US	-	-	46	91	13	n2p1+tp	19
96	Peter Sarnak	Princeton University	US	-	-	25	-	57	n2p1	46
97	M. B. Milinovich	University of Mississippi	US	-	60	-	77	11	leg+tp	18
98	Valeriia Starichkova	UNSW Canberra	AU	96	-	-	50	2	gb+tp	3
99	Liqun Hu	Nanchang University	CN	29	-	-	-	5	gb	-
100	Lior Bary-Soroker	Tel Aviv University	IL	-	-	-	45	10	gb+tp	18

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`	31
`gb+leg+tp`	16
`leg+tp`	11
`gb+n2p1`	9
`gb`	6
`gb+tp`	6
`leg+n2p1+tp`	4
`gb+n2p1+tp`	3
`gb+leg+n2p1`	3
`n2p1`	3
`n2p1+tp`	2
`gb+leg`	2
`leg+n2p1`	2
`leg`	2

Limitations

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