Prime p₀= 2338763481001856141 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 4 2 10 2 28 2 46 2 70 2 (?)
a_n: 0 2 30 32 36 38 48 50 78 80 126 128 198 200
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: 200
Found by: Landjunge
db: batch=81, k=14, 28 4 10 28 46 70

SPT(16)	2338762346639863517	0 36 62 102 114 156 170 174 242 246 260 302 314 354 380 416	-1134361992624
STPT(10)	2338762535026604369	0 2 42 44 90 92 138 140 180 182	-945975251772
STPT(10)	2338762713048909479	0 2 48 50 90 92 132 134 180 182	-767952946662
SPT(16)	2338762833451710511	0 28 42 46 72 82 112 132 136 156 186 196 222 226 240 268	-647550145630
SPT(16)	2338762956634570513	0 48 54 64 84 94 150 160 168 178 234 244 264 274 280 328	-524367285628
STPT(10)	2338763048487242129	0 2 18 20 30 32 42 44 60 62	-432514614012
SPT(16)	2338763502820020167	0 6 20 72 140 150 162 170 216 224 236 246 314 366 380 386	21818164026
SPT(16)	2338763513359172891	0 12 66 102 120 140 158 168 200 210 228 248 266 302 356 368	32357316750
STPT(10)	2338763750138726087	0 2 60 62 72 74 84 86 144 146	269136869946
STPT(10)	2338764756649059689	0 2 18 20 30 32 42 44 60 62	1275647203548
SPT(16)	2338764798886948903	0 48 70 78 100 148 216 228 256 268 336 384 406 414 436 484	1317885092762