Prime p₀= 1123355878913603519 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 28 2 10 2 76 2 10 2 28 2 (?)
a_n: 0 2 30 32 42 44 120 122 132 134 162 164
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: mikey
db: batch=76, k=12, 2 28 2 10 2 76

SPT(16)	1123354576244187901	0 40 42 48 52 60 66 102 196 232 238 246 250 256 258 298	-1302669415618
STPT(10)	1123354646595754121	0 2 6 8 48 50 90 92 96 98	-1232317849398
SPT(16)	1123355025372445703	0 14 50 66 74 80 96 120 140 164 180 186 194 210 246 260	-853541157816
TPT(14)	1123355167626063089	0 2 12 14 90 92 168 170 240 242 300 302 390 392	-711287540430
STPT(10)	1123355701144145471	0 2 30 32 60 62 90 92 120 122	-177769458048
STPT(10)	1123355787680272379	0 2 48 50 60 62 72 74 120 122	-91233331140
SPT(16)	1123355927893647557	0 72 84 96 116 120 134 174 182 222 236 240 260 272 284 356	48980044038
STPT(10)	1123355952852609569	0 2 42 44 60 62 78 80 120 122	73939006050
SPT(16)	1123356294064920187	0 70 72 82 126 132 166 184 192 210 244 250 294 304 306 376	415151316668
SPT(16)	1123356336911962781	0 36 62 66 78 90 96 146 222 272 278 290 302 306 332 368	457998359262
SPT(16)	1123356983987522521	0 30 52 66 70 90 108 130 138 160 178 198 202 216 238 268	1105073919002