Prime p₀= 794119366564087997 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 10 2 4 2 10 2 10 2 (?)
a_n: 0 2 12 14 24 26 30 32 42 44 54 56
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: 56
Found by: [SG]FX
db: batch=73, k=12, 2 10 2 10 2 4

SPT(16)	794118933245187023	0 14 90 96 138 158 168 200 204 236 246 266 308 314 390 404	-433318900974
STPT(10)	794119004164918259	0 2 42 44 60 62 78 80 120 122	-362399169738
SPT(16)	794119112139280397	0 2 12 44 74 110 140 164 240 264 294 330 360 392 402 404	-254424807600
TPT(14)	794119123449379619	0 2 12 14 48 50 90 92 108 110 132 134 138 140	-243114708378
SPT(16)	794119319647646051	0 2 42 48 80 120 126 132 206 212 218 258 290 296 336 338	-46916441946
SPT(16)	794119330880109043	0 18 66 124 148 150 154 160 264 270 274 276 300 358 406 424	-35683978954
STPT(10)	794119828222704197	0 2 30 32 42 44 54 56 84 86	461658616200
SPT(16)	794120542166749531	0 6 30 108 142 160 166 180 298 312 318 336 370 448 472 478	1175602661534
SPT(16)	794120547878022461	0 38 78 92 98 162 176 180 188 192 206 270 276 290 330 368	1181313934464
SPT(20)	794120944835163373	0 18 58 106 120 168 186 190 198 204 220 226 234 238 256 304 318 366 406 424	1578271075376
STPT(12)	794121549026894069	0 2 18 20 42 44 78 80 102 104 120 122	2182462806072