Prime p₀= 1122720173429435687 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 16 2 22 2 16 2 10 2 (?)
a_n: 0 2 12 14 30 32 54 56 72 74 84 86
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: 86
Found by: crashtech
db: batch=76, k=12, 2 10 2 16 2 22

SPT(16)	1122718238740622197	0 4 24 46 64 76 126 130 150 154 204 216 234 256 276 280	-1934688813490
STPT(10)	1122718469361155657	0 2 12 14 42 44 72 74 84 86	-1704068280030
STPT(10)	1122718557302198609	0 2 18 20 30 32 42 44 60 62	-1616127237078
SPT(16)	1122718732090793317	0 6 34 64 72 102 112 142 174 204 214 244 252 282 310 316	-1441338642370
SPT(16)	1122719365029073733	0 20 26 36 48 50 126 138 218 230 306 308 320 330 336 356	-808400361954
SPT(16)	1122720053055508267	0 10 52 90 114 132 142 154 180 192 202 220 244 282 324 334	-120373927420
STPT(10)	1122720197704530167	0 2 12 14 42 44 72 74 84 86	24275094480
STPT(10)	1122720469965206009	0 2 18 20 30 32 42 44 60 62	296535770322
STPT(10)	1122721005111265457	0 2 42 44 72 74 102 104 144 146	831681829770
SPT(16)	1122721407369524311	0 16 18 42 72 88 96 108 130 142 150 166 196 220 222 238	1233940088624
STPT(10)	1122721829027695031	0 2 36 38 78 80 120 122 156 158	1655598259344