Prime p₀= 726838783114752437 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 118 2 10 2 28 2 10 2 118 2 (?)
a_n: 0 2 120 122 132 134 162 164 174 176 294 296
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: 296
Found by: Theadalus
db: batch=73, k=12, 2 118 2 10 2 28

SPT(16)	726838145265699787	0 12 24 42 84 94 102 126 130 154 162 172 214 232 244 256	-637849052650
SPT(16)	726838156248240679	0 18 84 90 100 108 142 174 178 210 244 252 262 268 334 352	-626866511758
TPT(14)	726838284311297441	0 2 6 8 96 98 126 128 138 140 288 290 546 548	-498803454996
STPT(10)	726838458650457029	0 2 30 32 60 62 90 92 120 122	-324464295408
SPT(16)	726838596671166169	0 22 84 94 112 114 124 138 154 168 178 180 198 208 270 292	-186443586268
SPT(16)	726838743942552679	0 22 48 54 58 64 78 84 118 124 138 144 148 154 180 202	-39172199758
SPT(16)	726838984505790479	0 30 50 60 68 74 78 102 110 134 138 144 152 162 182 212	201391038042
SPT(18)	726839302177281971	0 12 18 30 32 38 56 98 150 188 240 282 300 306 308 320 326 338	519062529534
SPT(16)	726839659198455071	0 2 38 78 80 176 188 206 222 240 252 348 350 390 426 428	876083702634
STPT(10)	726841115773941977	0 2 12 14 72 74 132 134 144 146	2332659189540
TPT(14)	726841157845523549	0 2 12 14 78 80 108 110 288 290 372 374 420 422	2374730771112