Prime p₀= 1208142667329448427 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 76 2 10 2 58 2 106 2 82 2 (?)
a_n: 0 2 42 44 120 122 132 134 192 194 300 302 384 386
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: 386
Found by: Megacruncher
db: batch=77, k=14, 40 76 10 58 106 82

SPT(16)	1208140696650846121	0 28 36 120 168 192 196 238 360 402 406 430 478 562 570 598	-1970678602306
STPT(10)	1208141821996573127	0 2 42 44 72 74 102 104 144 146	-845332875300
TPT(14)	1208142085743419291	0 2 78 80 90 92 108 110 168 170 180 182 210 212	-581586029136
SPT(16)	1208142455092306999	0 18 28 52 90 118 130 172 180 222 234 262 300 324 334 352	-212237141428
SPT(16)	1208142506879828369	0 14 20 38 54 68 80 90 98 108 120 134 150 168 174 188	-160449620058
SPT(16)	1208142593121302417	0 24 42 80 96 126 216 264 272 320 410 440 456 494 512 536	-74208146010
STPT(10)	1208142811842117161	0 2 6 8 48 50 90 92 96 98	144512668734
SPT(16)	1208143012021610141	0 26 32 42 50 96 116 120 158 162 182 228 236 246 252 278	344692161714
STPT(10)	1208143114250424179	0 2 18 20 60 62 102 104 120 122	446920975752
SPT(16)	1208143352128345837	0 10 84 94 130 150 184 204 220 240 274 294 330 340 414 424	684798897410
STPT(10)	1208143432691774207	0 2 30 32 72 74 114 116 144 146	765362325780