Prime p₀= 1035669047448378599 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 4 2 22 2 4 2 10 2 (?)
a_n: 0 2 12 14 18 20 42 44 48 50 60 62
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: 62
Found by: stoneageman
db: batch=76, k=12, 2 10 2 4 2 22

SPT(16)	1035667858851661817	0 56 62 132 162 176 216 264 302 350 390 404 434 504 510 566	-1188596716782
STPT(10)	1035667871825163719	0 2 18 20 30 32 42 44 60 62	-1175623214880
SPT(16)	1035668114187006673	0 28 48 76 168 214 220 226 288 294 300 346 438 466 486 514	-933261371926
STPT(10)	1035668613837414911	0 2 6 8 48 50 90 92 96 98	-433610963688
STPT(10)	1035668720448339959	0 2 42 44 60 62 78 80 120 122	-327000038640
TPT(14)	1035669043556345687	0 2 12 14 24 26 84 86 150 152 192 194 222 224	-3892032912
SPT(16)	1035669243089547271	0 28 46 58 126 132 150 156 232 238 256 262 330 342 360 388	195641168672
STPT(10)	1035669323373923177	0 2 30 32 60 62 90 92 120 122	275925544578
STPT(10)	1035669445100119901	0 2 36 38 78 80 120 122 156 158	397651741302
STPT(10)	1035669614813862617	0 2 30 32 42 44 54 56 84 86	567365484018
SPT(16)	1035670382731274177	0 20 54 72 104 122 132 140 156 164 174 192 224 242 276 296	1335282895578