Prime p₀= 2725814541311464151 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 58 2 154 2 52 2 16 2 10 2 (?)
a_n: 0 2 90 92 150 152 306 308 360 362 378 380 390 392
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: 392
Found by: JayPi
db: batch=82, k=14, 88 58 154 52 16 10

SPT(16)	2725812213107084687	0 42 60 66 92 104 134 152 174 192 222 234 260 266 284 326	-2328204379464
STPT(10)	2725812524310490001	0 2 30 32 78 80 126 128 156 158	-2017000974150
SPT(16)	2725812642072792907	0 24 46 70 94 162 196 214 252 270 304 372 396 420 442 466	-1899238671244
STPT(10)	2725813461865157687	0 2 72 74 102 104 132 134 204 206	-1079446306464
SPT(16)	2725814254426022801	0 20 26 56 66 90 108 116 132 140 158 182 192 222 228 248	-286885441350
SPT(16)	2725814439980518013	0 8 30 54 56 78 138 156 248 266 326 348 350 374 396 404	-101330946138
SPT(16)	2725814958482838671	0 26 42 78 116 122 126 182 306 362 366 372 410 446 462 488	417171374520
SPT(16)	2725815368510223089	0 20 38 62 72 92 128 144 188 204 240 260 270 294 312 332	827198758938
SPT(16)	2725815391023738329	0 30 60 78 114 138 144 180 182 218 224 248 284 302 332 362	849712274178
STPT(10)	2725815535050884369	0 2 42 44 60 62 78 80 120 122	993739420218
TPT(14)	2725815609917021201	0 2 150 152 240 242 318 320 360 362 378 380 396 398	1068605557050