Prime p₀= 2032094153668269329 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 70 2 34 2 28 2 112 2 58 2 (?)
a_n: 0 2 60 62 132 134 168 170 198 200 312 314 372 374
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: 374
Found by: Landjunge
db: batch=80, k=14, 58 70 34 28 112 58

SPT(16)	2032093505249468099	0 18 20 62 104 132 174 192 350 368 410 438 480 522 524 542	-648418801230
SPT(16)	2032093796053110271	0 6 16 42 52 72 118 132 136 150 196 216 226 252 262 268	-357615159058
TPT(14)	2032093843109298929	0 2 72 74 78 80 102 104 312 314 408 410 420 422	-310558970400
SPT(16)	2032093850362404599	0 8 42 78 102 110 134 140 162 168 192 200 224 260 294 302	-303305864730
STPT(10)	2032093891089303029	0 2 18 20 30 32 42 44 60 62	-262578966300
SPT(16)	2032093998090406093	0 6 16 46 60 64 84 114 130 160 180 184 198 228 238 244	-155577863236
STPT(10)	2032094167535721941	0 2 36 38 78 80 120 122 156 158	13867452612
SPT(16)	2032094257716353837	0 14 86 90 212 276 320 350 366 396 440 504 626 630 702 716	104048084508
SPT(16)	2032094417889621431	0 2 68 78 110 132 140 162 188 210 218 240 272 282 348 350	264221352102
SPT(16)	2032094774170771073	0 18 24 74 78 84 114 140 144 170 200 206 210 260 266 284	620502501744
SPT(16)	2032095010920665849	0 30 42 48 110 158 188 222 230 264 294 342 404 410 422 452	857252396520