Prime p₀= 1295675625307368629 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 16 2 22 2 34 2 22 2 16 2 (?)
a_n: 0 2 18 20 42 44 78 80 102 104 120 122
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: 122
Found by: Cruncher Pete
db: batch=77, k=12, 2 16 2 22 2 34

SPT(16)	1295673255639313843	0 34 48 70 84 90 106 108 136 138 154 160 174 196 210 244	-2369668054786
STPT(10)	1295673266320699727	0 2 24 26 42 44 60 62 84 86	-2358986668902
SPT(16)	1295674083477467233	0 24 28 60 108 154 180 184 234 238 264 310 358 390 394 418	-1541829901396
SPT(16)	1295675273109568097	0 24 50 62 92 132 140 152 162 174 182 222 252 264 290 314	-352197800532
SPT(16)	1295675317534100513	0 14 80 86 98 138 150 168 176 194 206 246 258 264 330 344	-307773268116
SPT(16)	1295675322223847651	0 56 86 120 128 158 162 182 186 206 210 240 248 282 312 368	-303083520978
STPT(10)	1295675853785457437	0 2 42 44 72 74 102 104 144 146	228478088808
SPT(16)	1295675929866586817	0 2 30 42 44 54 72 96 110 134 152 162 164 176 204 206	304559218188
SPT(16)	1295675955733695253	0 40 64 76 78 84 124 154 210 240 280 286 288 300 324 364	330426326624
STPT(10)	1295676324982975751	0 2 6 8 48 50 90 92 96 98	699675607122
SPT(16)	1295676370870907651	0 48 62 68 86 90 138 146 162 170 218 222 240 246 260 308	745563539022