Prime p₀= 2159912207775172271 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 40 2 40 2 4 2 28 2 10 2 (?)
a_n: 0 2 36 38 78 80 120 122 126 128 156 158 168 170
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: 170
Found by: Landjunge
db: batch=81, k=14, 34 40 40 4 28 10

SPT(16)	2159911246045197487	0 10 64 82 94 124 126 156 160 190 192 222 234 252 306 316	-961729974784
STPT(10)	2159911259238768941	0 2 6 8 48 50 90 92 96 98	-948536403330
SPT(16)	2159911605207626173	0 4 28 78 120 144 148 190 294 336 340 364 406 456 480 484	-602567546098
SPT(18)	2159911922157721639	0 48 64 88 90 150 160 178 180 202 204 222 232 292 294 318 334 382	-285617450632
SPT(16)	2159911938109578743	0 6 24 56 104 110 150 156 224 230 270 276 324 356 374 380	-269665593528
STPT(10)	2159912026898096459	0 2 18 20 30 32 42 44 60 62	-180877075812
SPT(16)	2159912671865490797	0 2 62 90 92 126 132 140 156 164 170 204 206 234 294 296	464090318526
SPT(16)	2159912920787632831	0 28 42 60 72 112 142 148 150 156 186 226 238 256 270 298	713012460560
STPT(10)	2159913078022618727	0 2 30 32 42 44 54 56 84 86	870247446456
STPT(10)	2159913215236359617	0 2 60 62 72 74 84 86 144 146	1007461187346
TPT(14)	2159913357107571827	0 2 114 116 234 236 240 242 324 326 390 392 450 452	1149332399556