Prime p₀= 957486140098688201 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 46 2 10 2 166 2 22 2 76 2 (?)
a_n: 0 2 78 80 126 128 138 140 306 308 330 332 408 410
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: 410
Found by: Theadalus
db: batch=76, k=14, 76 46 10 166 22 76

SPT(16)	957484093719753217	0 16 22 34 72 90 126 132 184 190 226 244 282 294 300 316	-2046378934984
SPT(16)	957484487557222061	0 12 62 92 98 138 150 182 258 290 302 342 348 378 428 440	-1652541466140
SPT(16)	957484578111750379	0 10 12 40 42 52 70 78 124 132 150 160 162 190 192 202	-1561986937822
TPT(14)	957484845638743067	0 2 60 62 84 86 162 164 204 206 240 242 270 272	-1294459945134
TPT(14)	957484880811064217	0 2 42 44 84 86 132 134 150 152 252 254 294 296	-1259287623984
SPT(16)	957485978171567477	0 14 42 72 80 114 120 140 246 266 272 306 314 344 372 386	-161927120724
SPT(16)	957486433584112147	0 22 60 160 162 190 202 234 322 354 366 394 396 496 534 556	293485423946
SPT(16)	957486826880417089	0 22 40 42 64 70 102 114 130 142 174 180 202 204 222 244	686781728888
STPT(10)	957486976877956697	0 2 30 32 42 44 54 56 84 86	836779268496
STPT(10)	957487018509072809	0 2 18 20 30 32 42 44 60 62	878410384608
SPT(16)	957487229861399539	0 24 60 70 84 100 102 112 252 262 264 280 294 304 340 364	1089762711338