Prime p₀= 976934544536149697 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 88 2 4 2 70 2 46 2 10 2 (?)
a_n: 0 2 24 26 114 116 120 122 192 194 240 242 252 254
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: 254
Found by: [SG-2W]Kurzer
db: batch=76, k=14, 22 88 4 70 46 10

SPT(16)	976933688366498407	0 12 52 96 100 102 114 180 226 292 304 306 310 354 394 406	-856169651290
STPT(10)	976933699122124241	0 2 36 38 78 80 120 122 156 158	-845414025456
SPT(16)	976933849591568083	0 28 40 54 88 94 118 130 174 186 210 216 250 264 276 304	-694944581614
STPT(10)	976933938505227881	0 2 6 8 48 50 90 92 96 98	-606030921816
SPT(16)	976934320869155417	0 6 30 44 86 96 104 146 264 306 314 324 366 380 404 410	-223666994280
TPT(14)	976934434115095241	0 2 30 32 36 38 156 158 210 212 240 242 300 302	-110421054456
STPT(10)	976934717812932161	0 2 6 8 48 50 90 92 96 98	173276782464
SPT(16)	976934988095811331	0 52 90 96 112 126 160 166 186 192 226 240 256 262 300 352	443559661634
SPT(16)	976935073691393959	0 4 24 28 42 64 72 88 174 190 198 220 234 238 258 262	529155244262
SPT(16)	976935198550308677	0 36 42 86 116 140 150 162 164 176 186 210 240 284 290 326	654014158980
STPT(10)	976935591451208339	0 2 18 20 30 32 42 44 60 62	1046915058642