Prime p₀= 1539254127182931617 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 28 2 76 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 120 122 150 152 162 164
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: 164
Found by: crashtech
db: batch=78, k=12, 2 10 2 28 2 76

STPT(10)	1539252343422253487	0 2 24 26 42 44 60 62 84 86	-1783760678130
STPT(10)	1539252753758048669	0 2 18 20 30 32 42 44 60 62	-1373424882948
TPT(14)	1539253182445475129	0 2 42 44 78 80 90 92 162 164 222 224 252 254	-944737456488
SPT(16)	1539253236165754339	0 24 28 52 58 72 90 154 198 262 280 294 300 324 328 352	-891017177278
SPT(16)	1539253459700892713	0 24 50 68 84 128 134 144 260 270 276 320 336 354 380 404	-667482038904
SPT(16)	1539253604057372641	0 22 102 120 142 166 168 256 282 370 372 396 418 436 516 538	-523125558976
SPT(16)	1539254143469525051	0 6 38 62 86 92 108 116 132 140 156 162 186 210 242 248	16286593434
STPT(10)	1539254504864055191	0 2 36 38 78 80 120 122 156 158	377681123574
SPT(16)	1539254533122165131	0 18 38 60 110 150 182 186 272 276 308 348 398 420 440 458	405939233514
TPT(14)	1539254561756453207	0 2 12 14 30 32 72 74 120 122 180 182 210 212	434573521590
SPT(16)	1539254786190852793	0 24 76 96 124 150 166 216 298 348 364 390 418 438 490 514	659007921176