Prime p₀= 726741936583087487 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: Theadalus
db: batch=73, k=12, 2 10 2 16 2 22

STPT(12)	726740119166883959	0 2 12 14 42 44 60 62 90 92 102 104	-1817416203528
TPT(14)	726740119166883959	0 2 12 14 42 44 60 62 90 92 102 104 132 134	-1817416203528
SPT(16)	726740207305000697	0 2 42 86 194 200 224 252 284 312 336 342 450 494 534 536	-1729278086790
STPT(10)	726740539283180921	0 2 36 38 78 80 120 122 156 158	-1397299906566
SPT(16)	726741052903063379	0 2 24 54 60 62 84 104 108 128 150 152 158 188 210 212	-883680024108
STPT(10)	726741605874828461	0 2 30 32 78 80 126 128 156 158	-330708259026
SPT(16)	726741992882539801	0 10 12 40 46 52 96 100 138 142 186 192 198 226 228 238	56299452314
SPT(16)	726742051995217381	0 18 120 148 160 166 172 186 232 246 252 258 270 298 400 418	115412129894
SPT(16)	726742170136236647	0 26 30 56 72 92 156 162 170 176 240 260 276 302 306 332	233553149160
SPT(16)	726742229704421239	0 24 28 64 70 78 112 138 154 180 214 222 228 264 268 292	293121333752
STPT(10)	726742316529712667	0 2 30 32 60 62 90 92 120 122	379946625180