Prime p₀= 976167570682400021 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 34 2 82 2 16 2 70 2 76 2 (?)
a_n: 0 2 90 92 126 128 210 212 228 230 300 302 378 380
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: 380
Found by: stoneageman
db: batch=76, k=14, 88 34 82 16 70 76

SPT(16)	976167075531720473	0 24 30 36 56 74 104 120 170 186 216 234 254 260 266 290	-495150679548
SPT(16)	976167276753651473	0 38 50 60 78 80 110 144 200 234 264 266 284 294 306 344	-293928748548
SPT(16)	976167339557297207	0 12 42 60 92 110 134 144 182 192 216 234 266 284 314 326	-231125102814
STPT(10)	976167370797152927	0 2 30 32 42 44 54 56 84 86	-199885247094
SPT(16)	976167478626908857	0 34 64 144 150 172 190 196 210 216 234 256 262 342 372 406	-92055491164
SPT(16)	976167489210774671	0 12 30 42 72 110 158 170 210 222 270 308 338 350 368 380	-81471625350
SPT(16)	976167617475167869	0 10 52 58 64 90 94 108 124 138 142 168 174 180 222 232	46792767848
STPT(10)	976168072898556047	0 2 42 44 72 74 102 104 144 146	502216156026
TPT(14)	976168195329289871	0 2 60 62 96 98 138 140 150 152 186 188 228 230	624646889850
SPT(16)	976168617947835269	0 2 20 42 72 84 102 104 138 140 158 170 200 222 240 242	1047265435248
SPT(16)	976168637380877987	0 2 26 30 104 114 132 144 182 194 212 222 296 300 324 326	1066698477966