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	1	2	-	1	26	gb+leg+tp	50
2	Kaisa Matomäki	University of Turku	FI	20	1	26	2	16	gb+leg+n2p1+tp	17
3	Terence Tao	University of California, Los Angeles	US	11	3	34	3	101	gb+leg+n2p1+tp	30
4	Florian Luca	Stellenbosch University	ZA	74	6	2	5	28	gb+leg+n2p1+tp	30
5	Daniel A. Goldston	San Jose State University	US	6	4	-	4	21	gb+leg+tp	45
6	D. R. Heath-Brown	University of Oxford	GB	61	5	4	9	45	gb+leg+n2p1+tp	47
7	Joni Teräväinen	University of Cambridge	GB	5	18	30	6	9	gb+leg+n2p1+tp	8
8	Glyn Harman	Royal Holloway University of London	GB	21	8	6	19	19	gb+leg+n2p1+tp	44
9	Henryk Iwaniec	Rutgers University	US	68	17	1	24	50	gb+leg+n2p1+tp	54
10	Stephan Baier	Ramakrishna Mission Vivekananda Educational and Research Institute	IN	10	32	8	16	14	gb+leg+n2p1+tp	26
11	John B. Friedlander	University of Toronto	CA	54	13	3	21	34	gb+leg+n2p1+tp	54
12	James Maynard	University of Oxford	GB	27	12	23	7	11	gb+leg+n2p1+tp	13
13	Jörg Brüdern	University of Göttingen	DE	3	40	40	42	19	gb+leg+n2p1+tp	38
14	Runbo Li	University of Michigan	US	60	10	18	12	-	gb+leg+n2p1+tp	-
15	Alessandro Languasco	University of Padua	IT	17	9	-	8	12	gb+leg+tp	30
16	Carl Pomerance	Dartmouth College	US	92	11	12	22	39	gb+leg+n2p1+tp	54
17	Paul Pollack	University of Georgia	US	-	21	13	10	13	gb+leg+n2p1+tp	18
18	Alessandro Zaccagnini	University of Parma	IT	16	7	-	17	14	gb+leg+tp	32
19	Etienne Fouvry	Université Paris-Saclay	FR	-	23	11	15	28	gb+leg+n2p1+tp	45
20	Kevin Ford	University of Illinois Urbana-Champaign	US	34	19	27	11	-	gb+leg+n2p1+tp	32
21	Igor E. Shparlinski	UNSW Sydney	AU	7	-	7	-	42	gb+n2p1	46
22	Trevor D. Wooley	Purdue University West Lafayette	US	2	81	64	-	28	gb+leg+n2p1+tp	36
23	Andrew Granville	Université de Montréal	CA	39	25	14	35	32	gb+leg+n2p1+tp	39
24	M. Ram Murty	Queen's University	CA	88	-	5	25	25	gb+n2p1+tp	46
25	Jie Wu	Centre National de la Recherche Scientifique	FR	-	22	17	27	19	gb+leg+n2p1+tp	21
26	Yoichi Motohashi	Nihon University	JP	-	71	9	26	19	gb+leg+n2p1+tp	-
27	K. Soundararajan	Stanford University	US	-	14	58	13	33	leg+n2p1+tp	28
28	Harold G. Diamond	University of Illinois Urbana-Champaign	US	-	34	31	14	19	leg+n2p1+tp	61
29	Alberto Perelli	University of Genoa	IT	18	37	65	39	20	gb+leg+n2p1+tp	50
30	Jianya Liu	Shandong University	CN	8	65	-	71	14	gb+leg+tp	31
31	Dieter Wolke	University of Freiburg	DE	64	28	38	29	-	gb+leg+n2p1+tp	57
32	William D. Banks	University of Missouri	US	23	61	46	28	21	gb+leg+n2p1+tp	32
33	R. C. Vaughan	Pennsylvania State University	US	12	-	22	-	35	gb+n2p1	56
34	Jinjiang Li	China University of Mining and Technology (Beijing)	CN	4	-	-	-	6	gb	-
35	Hugh Lowell Montgomery	University of Michigan	US	38	56	41	32	32	gb+leg+n2p1+tp	54
36	Xuancheng Shao	University of Kentucky	US	15	41	-	47	10	gb+leg+tp	12
37	Angel Kumchev	Towson University	US	26	52	37	60	12	gb+leg+n2p1+tp	25
38	Ofir Gorodetsky	Technion - Israel Institute of Technology	IL	-	15	-	18	5	leg+tp	5
39	Jori Merikoski	University of Helsinki	FI	30	48	61	33	2	gb+leg+n2p1+tp	5
40	Efthymios Sofos	University of Glasgow	GB	86	94	10	-	7	gb+leg+n2p1	11
41	Hao Pan	Nanjing University of Finance and Economics	CN	43	70	43	40	17	gb+leg+n2p1+tp	20
42	Chaohua Jia	Chinese Academy of Sciences	CN	36	31	-	36	11	gb+leg+tp	39
43	Brad Rodgers	Queen's University	CA	-	16	-	30	8	leg+tp	13
44	Alexandru Zaharescu	University of Illinois Urbana-Champaign	US	32	45	71	82	24	gb+leg+n2p1+tp	35
45	Adrian Dudek	University of Queensland	AU	52	27	-	43	5	gb+leg+tp	10
46	Emmanuel Kowalski	ETH Zurich	CH	81	63	35	70	29	gb+leg+n2p1+tp	28
47	Tianze Wang	Henan Academy of Sciences	CN	9	-	-	-	2	gb	35
48	Jesse Thorner	University of Illinois Urbana-Champaign	US	-	24	87	58	9	leg+n2p1+tp	10
49	Roger C. Baker	Brigham Young University	US	66	30	-	49	34	gb+leg+tp	55
50	Antal Balog	Alfréd Rényi Institute of Mathematics	HU	63	68	47	81	18	gb+leg+n2p1+tp	35
51	Victor Volfson	-	RU	-	-	16	-	0	gb+n2p1+tp	-
52	Vivian Kuperberg	ETH Zurich	CH	-	38	-	23	3	leg+tp	4
53	András Sárközy	Eötvös Loránd University	HU	25	-	28	-	31	gb+n2p1	57
54	Helmut Maier	Universität Ulm	DE	44	49	-	51	18	gb+leg+tp	45
55	Yu-Chen Sun	University of Turku	FI	-	33	-	31	-	leg+tp	5
56	Stephan Ramon Garcia	Pomona College	US	-	-	24	45	27	n2p1+tp	23
57	Doychin Tolev	Sofia University "St. Kliment Ohridski"	BG	56	-	39	61	10	gb+n2p1+tp	25
58	Peter D. T. A. Elliott	University of Colorado Boulder	US	97	-	15	-	19	gb+n2p1	57
59	Hongze Li	Shanghai Jiao Tong University	CN	40	58	-	55	-	gb+leg+tp	36
60	Michael Th. Rassias	Hellenic Military Academy	GR	65	55	-	41	24	gb+leg+tp	12
61	S. Salerno	University of Salerno	IT	-	73	55	54	-	leg+n2p1+tp	-
62	Lasse Grimmelt	University of Cambridge	GB	29	-	91	64	2	gb+n2p1+tp	7
63	Sergey Konyagin	Steklov Mathematical Institute	RU	-	36	42	-	28	leg+n2p1	44
64	Greg Martin	University of British Columbia	CA	72	75	77	-	16	gb+leg+n2p1+tp	29
65	Jiseong Kim	University of Mississippi	US	53	26	-	-	20	gb+leg	3
66	Jared Duker Lichtman	Stanford University	US	19	-	-	91	4	gb+tp	3
67	Min Zhang	Beijing Information Science and Technology University	CN	13	-	-	-	44	gb	-
68	Timothy S. Trudgian	Australian National University	AU	95	84	80	90	13	gb+leg+n2p1+tp	16
69	Wenguang Zhai	China University of Mining and Technology (Beijing)	CN	87	53	59	-	13	gb+leg+n2p1	30
70	V. N. Chubarikov	Lomonosov Moscow State University	RU	14	-	-	-	-	gb	49
71	S. W. Graham	Central Michigan University	US	-	82	57	73	15	leg+n2p1+tp	49
72	Ben Green	University of Oxford	GB	37	89	-	78	5	gb+leg+tp	23
73	Adolf Hildebrand	University of Illinois Urbana-Champaign	US	-	50	-	38	19	leg+tp	43
74	Jean‐Marc Deshouillers	Université de Bordeaux	FR	48	-	32	-	16	gb+n2p1	54
75	Cem Yalçın Yıldırım	Boğaziçi University	TR	-	64	-	34	2	leg+tp	36
76	Cameron L. Stewart	University of Waterloo	CA	-	46	52	-	20	leg+n2p1	50
77	Alexander K. Zvonkin	Université de Bordeaux	FR	-	-	19	-	12	n2p1	53
78	Régis de la Bretèche	Université Paris Cité	FR	-	66	76	-	14	leg+n2p1+tp	30
79	Matt Visser	Victoria University of Wellington	NZ	-	20	-	-	-	leg	42
80	J. P. Keating	University of Oxford	GB	-	59	-	44	40	leg+tp	37
81	Richard A. Mollin	University of Calgary	CA	-	-	20	-	18	n2p1	51
82	Giovanni Coppola	University of Salerno	IT	-	-	-	20	7	tp	-
83	Gérald Tenenbaum	Institut Élie Cartan de Lorraine	FR	-	-	21	-	30	n2p1	50
84	Tristan Freiberg	University of Waterloo	CA	-	47	-	66	4	leg+tp	16
85	S. I. Dimitrov	Technical University of Sofia	BG	31	-	68	-	6	gb+n2p1	-
86	Imre Kátai	Eötvös Loránd University	HU	78	-	36	-	15	gb+n2p1	60
87	Victor Zhenyu Guo	Xi'an Jiaotong University	CN	42	54	-	-	4	gb+leg	9
88	Yong-Gao Chen	Nanjing Normal University	CN	33	-	72	-	-	gb+n2p1	34
89	H. A. Helfgott	Université Paris Cité	FR	55	-	50	-	19	gb+n2p1	23
90	Felix Sidokhine	Independent	CA	-	57	-	63	-	leg+tp	-
91	George Greaves	University of Wales	GB	-	-	25	-	11	n2p1	-
92	Guangshi Lü	Shandong University	CN	89	44	-	-	17	gb+leg	22
93	Koichi Kawada	Iwate University	JP	46	-	67	-	9	gb+n2p1	32
94	D. Bazzanella	Politecnico di Torino	IT	-	60	-	75	-	leg+tp	30
95	Olivier Ramaré	Aix-Marseille Université	FR	75	-	-	48	15	gb+tp	35
96	Karin Halupczok	Heinrich Heine University Düsseldorf	DE	47	-	69	-	5	gb+n2p1	25
97	Jerzy Kaczorowski	Adam Mickiewicz University in Poznań	PL	99	43	-	-	19	gb+leg	43
98	Efrat Bank	Tel Aviv University	IL	-	29	-	-	3	leg	11
99	Alex Kontorovich	Rutgers University	US	-	-	51	98	13	n2p1+tp	19
100	Edva Roditty-Gershon	University of Bristol	GB	-	62	-	77	-	leg+tp	11

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`	32
`gb+leg+tp`	13
`gb+n2p1`	11
`leg+tp`	11
`leg+n2p1+tp`	6
`gb+n2p1+tp`	4
`gb`	4
`gb+leg`	4
`n2p1`	4
`gb+leg+n2p1`	2
`n2p1+tp`	2
`leg+n2p1`	2
`gb+tp`	2
`leg`	2
`tp`	1

Limitations

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