Prime p₀= 1278023421973830599 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 40 2 16 2 10 2 16 2 40 2 (?)
a_n: 0 2 42 44 60 62 72 74 90 92 132 134
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: 134
Found by: HenkM
db: batch=77, k=12, 2 40 2 16 2 10

STPT(10)	1278021925524056309	0 2 18 20 60 62 102 104 120 122	-1496449774290
TPT(14)	1278022419499355939	0 2 48 50 90 92 138 140 168 170 210 212 222 224	-1002474474660
SPT(16)	1278022676136114011	0 6 32 50 60 78 116 138 140 162 200 218 228 246 272 278	-745837716588
SPT(16)	1278023130801422197	0 40 70 96 106 154 166 174 322 330 342 390 400 426 456 496	-291172408402
STPT(10)	1278023179390493321	0 2 30 32 60 62 90 92 120 122	-242583337278
SPT(16)	1278023298314450771	0 18 80 98 102 158 186 210 248 272 300 356 360 378 440 458	-123659379828
SPT(16)	1278024601057421467	0 40 60 64 70 82 84 94 120 130 132 144 150 154 174 214	1179083590868
SPT(16)	1278024793547432159	0 20 84 110 132 140 152 224 228 300 312 320 342 368 432 452	1371573601560
SPT(16)	1278024884581512911	0 50 68 72 78 96 98 128 210 240 242 260 266 270 288 338	1462607682312
STPT(10)	1278024999717248591	0 2 6 8 48 50 90 92 96 98	1577743417992
SPT(16)	1278025194064834597	0 22 54 76 132 162 174 196 210 232 244 274 330 352 384 406	1772091003998