Prime p₀= 2398509316631123957 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 28 2 52 2 34 2 52 2 28 2 (?)
a_n: 0 2 30 32 84 86 120 122 174 176 204 206
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: 206
Found by: SEARCHER
db: batch=82, k=12, 2 28 2 52 2 34

STPT(10)	2398507949748712577	0 2 12 14 42 44 72 74 84 86	-1366882411380
STPT(10)	2398508256897189137	0 2 30 32 42 44 54 56 84 86	-1059733934820
SPT(16)	2398508352783420991	0 28 42 46 66 72 106 148 150 192 226 232 252 256 270 298	-963847702966
STPT(10)	2398508410825407701	0 2 6 8 18 20 30 32 36 38	-905805716256
STPT(10)	2398508539046528927	0 2 42 44 72 74 102 104 144 146	-777584595030
SPT(16)	2398508991435898507	0 34 60 64 90 102 112 124 132 144 154 166 192 196 222 256	-325195225450
SPT(16)	2398509638801264257	0 10 66 114 124 126 136 184 192 240 250 252 262 310 366 376	322170140300
STPT(10)	2398510644585034739	0 2 12 14 90 92 168 170 180 182	1327953910782
SPT(16)	2398511067589502821	0 16 30 40 48 88 106 130 156 180 198 238 246 256 270 286	1750958378864
STPT(10)	2398511209665673769	0 2 18 20 30 32 42 44 60 62	1893034549812
SPT(16)	2398511286619342397	0 12 62 90 132 150 174 180 194 200 224 242 284 312 362 374	1969988218440