Institutions

Where the twin prime conjecture research concentrates, three ways

Reading the columns

# the headline rank: the average of the Training and Environment scores shown in the next two columns. Average the two numbers on any row and the rows sort by exactly that average, so the # position is always explainable from what you see.
Training score from 0.00 to 1.00: where today's Top 100 earned their PhDs (verified Mathematics Genealogy records; 44 of 100 researchers covered), rank-weighted and scaled so the strongest training ground is 1.00. A dash means no recorded Top 100 alumni and counts as 0 in the average.
Environment score from 0.00 to 1.00: the research gravity around the institution today; every Top 100 researcher contributes by rank and by distance (exponential decay, 100 km scale), scaled so the strongest environment is 1.00. A dash means no verified coordinates yet and counts as 0.
Top 100 how many of the current Top 100 work there. Hover a row for names.
Institution names link to the institution's homepage (or its mathematics department where we have verified that page); links come from the institution's OpenAlex record.

Click any header to sort; the score columns sort strongest-first. Candidates are the union of the Top 100's current institutions and their PhD schools, so pure training grounds appear even when nobody on the list works there today.

#	Institution	Ctry	Top 100	Training	Environment
1	University of Cambridge	GB	1	0.99	0.70
2	Royal Holloway University of London	GB	1	0.86	0.81
3	University of Illinois Urbana-Champaign	US	4	0.43	0.91
4	Eötvös Loránd University	HU	1	0.75	0.57
5	Université de Montréal	CA	2	0.32	0.75
6	University of California, Berkeley	US	0	0.68	0.36
7	University of Genoa	IT	0	0.88	0.15
8	Université de Bordeaux	FR	0	1.00	0.01
9	University of Oxford	GB	3	-	1.00
10	Birkbeck, University of London	GB	0	0.20	0.68
11	Sorbonne Université	FR	0	0.26	0.53
12	University of Toronto	CA	1	0.34	0.42
13	Université du Québec à Montréal	CA	1	-	0.74
14	Université Paris-Saclay	FR	0	0.25	0.48
15	University of Michigan	US	3	0.00	0.71
16	Moscow State Pedagogical Institute	RU	0	0.48	0.22
17	University of Bristol	GB	0	0.18	0.52
18	University of California, Los Angeles	US	1	0.30	0.35
19	Queen's University	CA	1	0.32	0.31
20	University of Turku	FI	2	-	0.59
21	Alfréd Rényi Institute of Mathematics	HU	1	-	0.58
22	San Jose State University	US	1	-	0.57
23	Stanford University	US	1	-	0.57
24	Centre National de la Recherche Scientifique	FR	3	-	0.56
25	Shandong University	CN	1	0.51	0.04
26	University of New South Wales	AU	0	0.13	0.42
27	Northwestern University	US	1	-	0.53
28	University of Illinois Chicago	US	1	-	0.52
29	Queen's University at Kingston	CA	0	0.18	0.31
30	University of Göttingen	DE	1	0.27	0.22
31	University of Alaska, Fairbanks	US	0	0.48	0.00
32	Princeton University	US	1	-	0.48
33	Institute for Advanced Study	US	1	-	0.48
34	Rutgers University	US	1	-	0.48
35	Cardiff University	GB	1	-	0.47
36	University of Wales	GB	1	-	0.47
37	Philipps-Universität Marburg	DE	0	0.32	0.12
38	Universität Berlin	DE	0	0.41	0.03
39	University of Padua	IT	1	-	0.44
40	University of Waterloo	CA	2	-	0.42
41	UNSW Sydney	AU	2	-	0.42
42	Technische Universität Darmstadt	DE	0	0.28	0.13
43	Institut Élie Cartan de Lorraine	FR	1	-	0.41
44	University of Milan	IT	0	0.23	0.18
45	University of Parma	IT	1	-	0.40
46	Université Laval	CA	2	-	0.40
47	University of Salerno	IT	2	-	0.39
48	University of Freiburg	DE	1	-	0.37
49	Dartmouth College	US	1	-	0.36
50	Finnish Academy of Science and Letters	FI	1	-	0.35
51	Stellenbosch University	ZA	1	-	0.34
52	Lomonosov Moscow State University	RU	0	0.11	0.23
53	Tongji University	CN	1	-	0.34
54	Vilnius University	LT	1	-	0.34
55	Technion - Israel Institute of Technology	IL	1	-	0.34
56	Aix-Marseille Université	FR	1	-	0.34
57	Château Gombert	FR	1	-	0.33
58	University of Georgia	US	1	-	0.32
59	University of Colorado Boulder	US	1	-	0.31
60	Shanghai Jiao Tong University	CN	1	-	0.30
61	Durham University	GB	1	-	0.29
62	Ramakrishna Mission Vivekananda Educational and Research Institute	IN	1	-	0.29
63	University of Missouri	US	1	-	0.28
64	Tel Aviv University	IL	2	-	0.28
65	Graz University of Technology	AT	1	-	0.27
66	University of Lyon	FR	1	-	0.26
67	University of Wrocław	PL	1	-	0.26
68	Universität Ulm	DE	1	-	0.26
69	Beijing Information Science and Technology University	CN	1	-	0.25
70	China University of Mining and Technology (Beijing)	CN	1	-	0.25
71	State Key Laboratory of Cryptology	CN	1	-	0.24
72	Steklov Mathematical Institute	RU	1	-	0.24
73	Andhra University	IN	1	-	0.24
74	Butler University	US	1	-	0.23
75	University of Minnesota - Twin Cities	US	0	0.22	0.00
76	ETH Zurich	CH	1	-	0.22
77	Emory University	US	0	0.07	0.13
78	Institute of Technology	US	0	0.08	0.12
79	Pomona College	US	1	-	0.20
80	Abdus Salam International Centre for Theoretical Physics	IT	1	-	0.20
81	University of Kentucky	US	1	-	0.18
82	Sogang University	KR	1	-	0.18
83	Boğaziçi University	TR	1	-	0.17
84	Central Michigan University	US	1	-	0.17
85	University of South Carolina	US	0	0.13	0.04
86	Heinrich Heine University Düsseldorf	DE	1	-	0.16
87	Towson University	US	1	-	0.16
88	Allscripts (United States)	US	1	-	0.16
89	University of Zanjan	IR	1	-	0.15
90	Brigham Young University	US	1	-	0.14
91	University of Wisconsin-Madison	US	0	0.04	0.10
92	University of Canberra	AU	1	-	0.13
93	Tufts University	US	1	-	0.13
94	Victoria University of Wellington	NZ	1	-	0.12
95	Rikkyo University	JP	1	-	0.12
96	Brown University	US	1	-	0.10
97	Hellenic Military Academy	GR	1	-	0.09
98	University of Waikato	NZ	1	-	0.08
99	Sofia University "St. Kliment Ohridski"	BG	1	-	0.08
100	Indian Institute of Technology Bombay	IN	1	-	0.07
101	University, New Brunswick	CA	0	0.03	0.01
102	Chulalongkorn University	TH	1	-	0.04
103	University of Florida	US	1	-	0.01
104	Universidade Tecnologica Federal do Parana	BR	1	-	-