The big database of "The smallest prime k-tuplets"(compressed files) ←
last updated: 5 Dec 2021

k	first ... members	up to	pattern d	OEIS
2	1,000,000	2.52 • 108	d = 0, 2	A001359
3	1,000,000 1,000,000	3.12 • 109 3.12 • 109	d = 0, 2, 6 d = 0, 4, 6	A022004 A022005
4	1,000,000	7.95 • 1010	d = 0, 2, 6, 8	A007530
5	1,000,000 1,000,000	1.36 • 1012 1.36 • 1012	d = 0, 2, 6, 8, 12 d = 0, 4, 6, 10, 12	A022006 A022007
6	1,000,000	4.66 • 1013	d = 0, 4, 6, 10, 12, 16	A022008
7	1,000,000 1,000,000	8.21 • 1014 8.22 • 1014	d = 0, 2, 6, 8, 12, 18, 20 d = 0, 2, 8, 12, 14, 18, 20	A022009 A022010
8	10,000,000 10,000,000 10,000,000	3.08 • 1017 3.08 • 1017 8.93 • 1016	d = 0, 2, 6, 8, 12, 18, 20, 26 d = 0, 6, 8, 14, 18, 20, 24, 26 d = 0, 2, 6, 12, 14, 20, 24, 26	A022011 A022013 A022012
9	2,251,885 4,502,184 4,501,205 2,250,272	1018 1018 1018 1018	d = 0, 2, 6, 8, 12, 18, 20, 26, 30 d = 0, 2, 6, 12, 14, 20, 24, 26, 30 d = 0, 4, 6, 10, 16, 18, 24, 28, 30 d = 0, 4, 10, 12, 18, 22, 24, 28, 30	A022545 A022546 A022547 A022548
10	5,118,442 5,111,631	1020 1020	d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32 d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 32	A027569 A027570
11	205,272 206,279	1020 1020	d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36 d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 36	A213647 A213646
12	20,000 20,000	1.499 • 1020 1.478 • 1020	d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42 d = 0, 6, 10, 12, 16, 22, 24, 30, 34, 36, 40, 42	A213645 A213601
13	5,012 6,305 5,290 6,264 5,307 5,579	1.16 • 1021 1.29 • 1021 1.29 • 1021 1.29 • 1021 1.29 • 1021 1.32 • 1021	d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48 d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48 d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 36, 46, 48 d = 0, 2, 8, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48 d = 0, 2, 12, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48 d = 0, 6, 12, 16, 18, 22, 28, 30, 36, 40, 42, 46, 48	A257139 A257137 A257138 A257140 A257141 A214947
14	919 891	1022 1022	d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48, 50 d = 0, 2, 8, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48, 50	A257167 A257168
15	73 68 261 278	1022 1022 1022 1022	d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48, 50, 56 d = 0, 6, 8, 14, 20, 24, 26, 30, 36, 38, 44, 48, 50, 54, 56 d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 42, 44, 50, 54, 56 d = 0, 2, 6, 12, 14, 20, 26, 30, 32, 36, 42, 44, 50, 54, 56	A257304 A257307 A257305 A257306
16	30 37	1023 1023	d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60 d = 0, 2, 6, 12, 14, 20, 26, 30, 32, 36, 42, 44, 50, 54, 56, 60	A257369 A257370

More known initial prime k-tuplets