Prime p₀= 2156841478309349759 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 28 2 58 2 28 2 34 2 10 2 (?)
a_n: 0 2 12 14 42 44 102 104 132 134 168 170 180 182
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 182
Found by: Landjunge
db: batch=81, k=14, 10 28 58 28 34 10

TPT(14)	2156841061663078157	0 2 204 206 222 224 234 236 264 266 342 344 360 362	-416646271602
STPT(10)	2156841109851406829	0 2 12 14 90 92 168 170 180 182	-368457942930
SPT(16)	2156841198433237091	0 42 66 110 116 128 138 158 180 200 210 222 228 272 296 338	-279876112668
SPT(16)	2156841290013452719	0 4 10 42 48 138 144 150 232 238 244 334 340 372 378 382	-188295897040
SPT(16)	2156841335253177799	0 18 28 48 58 78 84 88 90 94 100 120 130 150 160 178	-143056171960
STPT(10)	2156841403767129971	0 2 90 92 108 110 126 128 216 218	-74542219788
SPT(16)	2156841629438784377	0 6 12 26 60 62 84 102 104 122 144 146 180 194 200 206	151129434618
SPT(16)	2156841806198305661	0 12 80 108 120 122 138 158 162 182 198 200 212 240 308 320	327888955902
SPT(16)	2156841893626902439	0 24 70 94 112 124 132 150 154 172 180 192 210 234 280 304	415317552680
SPT(16)	2156841915191121659	0 30 42 50 62 74 78 132 140 194 198 210 222 230 242 272	436881771900
STPT(10)	2156841946971098687	0 2 24 26 42 44 60 62 84 86	468661748928