Prime p₀= 1150518997959783677 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: Theadalus
db: batch=77, k=12, 2 10 2 10 2 4

SPT(16)	1150518292882182373	0 28 34 88 100 106 120 130 174 184 198 204 216 270 276 304	-705077601304
TPT(14)	1150518582952091261	0 2 30 32 186 188 210 212 240 242 276 278 348 350	-415007692416
SPT(16)	1150518604274292791	0 30 42 62 68 132 146 168 200 222 236 300 306 326 338 368	-393685490886
SPT(16)	1150518735970529287	0 6 40 52 60 64 102 120 136 154 192 196 204 216 250 256	-261989254390
TPT(14)	1150518757236543419	0 2 18 20 30 32 48 50 90 92 132 134 180 182	-240723240258
SPT(16)	1150518915298199633	0 14 44 50 60 84 116 168 176 228 260 284 294 300 330 344	-82661584044
TPT(14)	1150519515128403401	0 2 36 38 48 50 78 80 90 92 156 158 210 212	517168619724
STPT(10)	1150520187752909759	0 2 42 44 60 62 78 80 120 122	1189793126082
STPT(10)	1150520192996307389	0 2 12 14 90 92 168 170 180 182	1195036523712
TPT(14)	1150520212290594779	0 2 18 20 60 62 138 140 228 230 240 242 252 254	1214330811102
STPT(12)	1150520351081865887	0 2 12 14 54 56 90 92 132 134 144 146	1353122082210