Prime p₀= 1134105475996906409 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 70 2 10 2 4 2 22 2 58 2 (?)
a_n: 0 2 78 80 150 152 162 164 168 170 192 194 252 254
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: Alnitak2019
db: batch=76, k=14, 76 70 10 4 22 58

TPT(14)	1134104109538566251	0 2 96 98 150 152 198 200 246 248 288 290 348 350	-1366458340158
SPT(16)	1134104163422645489	0 2 12 20 32 50 68 92 180 204 222 240 252 260 270 272	-1312574260920
SPT(16)	1134104272851120083	0 6 18 38 84 104 128 144 170 186 210 230 276 296 308 314	-1203145786326
SPT(16)	1134104443490658149	0 2 38 42 44 48 68 102 110 144 164 168 170 174 210 212	-1032506248260
STPT(10)	1134104927687133287	0 2 12 14 42 44 72 74 84 86	-548309773122
SPT(16)	1134105213789530111	0 12 20 30 122 140 182 188 240 246 288 306 398 408 416 428	-262207376298
SPT(16)	1134106055932098481	0 22 46 82 102 108 136 162 196 222 250 256 276 312 336 358	579935192072
STPT(10)	1134106058701897667	0 2 12 14 42 44 72 74 84 86	582704991258
STPT(12)	1134106114928362991	0 2 30 32 60 62 126 128 156 158 186 188	638931456582
SPT(16)	1134106566630941741	0 8 12 32 48 50 66 102 266 302 318 320 336 356 360 368	1090634035332
SPT(16)	1134106813269468001	0 42 46 52 78 90 108 118 120 130 148 160 186 192 196 238	1337272561592