Prime p₀= 120088060632793439 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 40 2 16 2 28 2 76 2 10 2 (?)
a_n: 0 2 42 44 60 62 90 92 168 170 180 182
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: 182
Found by: bluestick.eu
db: batch=67, k=12, 40 16 28 76 10

SPT(14)	120087989601836369	0 38 42 44 72 84 92 150 158 170 198 200 204 242	-71030957070
SPT(14)	120087999381980051	0 2 8 38 60 102 122 126 146 188 210 240 246 248	-61250813388
SPT(14)	120088000560030469	0 40 52 114 120 124 142 150 168 172 178 240 252 292	-60072762970
SPT(14)	120088004740905247	0 36 72 124 126 156 210 226 280 310 312 364 400 436	-55891888192
SPT(16)	120088031773352191	0 22 42 48 58 82 96 118 120 142 156 180 190 196 216 238	-28859441248
SPT(14)	120088040638485481	0 28 46 66 70 78 90 106 118 126 130 150 168 196	-19994307958
TPT(12)	120088065568515479	0 2 12 14 30 32 42 44 78 80 120 122	4935722040
SPT(14)	120088067492468303	0 18 26 44 78 96 120 134 158 176 210 228 236 254	6859674864
SPT(14)	120088073571206359	0 10 12 34 112 154 190 222 258 300 378 400 402 412	12938412920
SPT(14)	120088074420524449	0 18 30 40 82 100 130 150 180 198 240 250 262 280	13787731010
SPT(14)	120088094274830089	0 4 48 64 88 90 102 160 172 174 198 214 258 262	33642036650