Prime p₀= 2582078465608989029 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 4 2 22 2 4 2 10 2 (?)
a_n: 0 2 12 14 18 20 42 44 48 50 60 62
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: 62
Found by: Penguin
db: batch=82, k=12, 2 10 2 4 2 22

SPT(16)	2582077286719815769	0 52 70 78 84 184 198 280 282 364 378 478 484 492 510 562	-1178889173260
SPT(16)	2582077303384494953	0 8 36 48 50 104 116 140 204 228 240 294 296 308 336 344	-1162224494076
SPT(16)	2582077400135721107	0 12 42 86 116 126 156 180 242 266 296 306 336 380 410 422	-1065473267922
SPT(16)	2582077911192501299	0 14 68 92 114 134 182 200 222 240 288 308 330 354 408 422	-554416487730
SPT(16)	2582078147462515601	0 6 26 30 48 78 110 146 162 198 230 260 278 282 302 308	-318146473428
SPT(16)	2582078429069035711	0 58 72 96 112 148 162 168 190 196 210 246 262 286 300 358	-36539953318
STPT(10)	2582079220599586847	0 2 42 44 72 74 102 104 144 146	754990597818
STPT(10)	2582080290824677829	0 2 18 20 30 32 42 44 60 62	1825215688800
STPT(10)	2582080379761422497	0 2 12 14 42 44 72 74 84 86	1914152433468
SPT(16)	2582080707838934201	0 6 12 50 96 120 230 240 242 252 362 386 432 470 476 482	2242229945172
STPT(10)	2582080839628356791	0 2 6 8 48 50 90 92 96 98	2374019367762