Prime p₀= 373548595079520407 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 28 2 10 2 238 2 76 2 28 2 (?)
a_n: 0 2 30 32 42 44 282 284 360 362 390 392
All 12 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 392
Found by: Aleksander Parkitny
db: batch=70, k=12, 28 10 238 76 28

SPT(14)	373548508787623181	0 8 12 18 26 62 78 80 96 132 140 146 150 158	-86291897226
SPT(16)	373548513427113733	0 48 76 78 130 168 198 238 246 286 316 354 406 408 436 484	-81652406674
SPT(14)	373548527365642667	0 12 20 26 30 56 62 174 180 206 210 216 224 236	-67713877740
SPT(14)	373548531921588631	0 6 40 82 100 132 166 252 286 318 336 378 412 418	-63157931776
SPT(14)	373548588312293111	0 2 6 42 48 68 152 156 240 260 266 302 306 308	-6767227296
SPT(14)	373548593838333629	0 8 14 24 72 92 114 128 150 170 218 228 234 242	-1241186778
SPT(16)	373548600348896549	0 2 62 80 104 108 128 150 152 174 194 198 222 240 300 302	5269376142
SPT(14)	373548617924567791	0 6 10 30 52 60 66 76 82 90 112 132 136 142	22845047384
SPT(14)	373548640147058237	0 24 30 42 66 72 96 110 134 140 164 176 182 206	45067537830
SPT(14)	373548649485454657	0 34 54 64 76 84 96 100 112 120 132 142 162 196	54405934250
SPT(14)	373548654406914799	0 4 102 112 168 208 220 222 234 274 330 340 438 442	59327394392