Prime p₀= 1235376602718032561 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 76 2 16 2 22 2 16 2 76 2 (?)
a_n: 0 2 78 80 96 98 120 122 138 140 216 218
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: 218
Found by: Cruncher Pete
db: batch=77, k=12, 2 76 2 16 2 22

TPT(14)	1235375240897851307	0 2 42 44 90 92 114 116 144 146 210 212 282 284	-1361820181254
STPT(10)	1235375377489690709	0 2 18 20 30 32 42 44 60 62	-1225228341852
STPT(10)	1235375971440855089	0 2 18 20 30 32 42 44 60 62	-631277177472
SPT(16)	1235376117355997093	0 8 50 54 60 80 114 138 140 164 198 218 224 228 270 278	-485362035468
SPT(16)	1235376220405420903	0 28 40 84 96 108 160 166 258 264 316 328 340 384 396 424	-382312611658
STPT(10)	1235376529617147821	0 2 36 38 78 80 120 122 156 158	-73100884740
SPT(16)	1235376703887750601	0 42 48 72 90 100 108 112 216 220 228 238 256 280 286 328	101169718040
STPT(10)	1235376984141998837	0 2 12 14 42 44 72 74 84 86	381423966276
SPT(16)	1235377018199890399	0 42 72 84 94 100 120 210 214 304 324 330 340 352 382 424	415481857838
STPT(10)	1235377025540253689	0 2 42 44 60 62 78 80 120 122	422822221128
STPT(10)	1235377128894306941	0 2 6 8 48 50 90 92 96 98	526176274380