Prime p₀= 1264393549404020669 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 28 2 100 2 4 2 100 2 28 2 (?)
a_n: 0 2 30 32 132 134 138 140 240 242 270 272
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: 272
Found by: Megacruncher
db: batch=77, k=12, 2 28 2 100 2 4

SPT(16)	1264392852438228803	0 50 68 78 80 108 134 138 176 180 206 234 236 246 264 314	-696965791866
SPT(16)	1264393225097524051	0 40 52 102 118 138 160 162 178 180 202 222 238 288 300 340	-324306496618
STPT(10)	1264393278889857827	0 2 42 44 72 74 102 104 144 146	-270514162842
STPT(10)	1264393339116953207	0 2 30 32 42 44 54 56 84 86	-210287067462
STPT(10)	1264393361198561651	0 2 36 38 78 80 120 122 156 158	-188205459018
STPT(10)	1264393480529433809	0 2 42 44 60 62 78 80 120 122	-68874586860
STPT(10)	1264393682803400057	0 2 30 32 42 44 54 56 84 86	133399379388
STPT(10)	1264393810372198871	0 2 30 32 78 80 126 128 156 158	260968178202
SPT(16)	1264393998088167481	0 16 36 82 96 106 126 132 316 322 342 352 366 412 432 448	448684146812
SPT(16)	1264394038133377673	0 18 30 36 56 60 110 168 188 246 296 300 320 326 338 356	488729357004
SPT(16)	1264394076945065069	0 14 24 78 104 108 128 150 152 174 194 198 224 278 288 302	527541044400