Prime p₀= 509500409142004517 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 10 2 10 2 28 2 94 2 28 2 (?)
a_n: 0 2 12 14 24 26 54 56 150 152 180 182
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: Rantanplan
db: batch=71, k=12, 10 10 28 94 28

SPT(16)	509500328636037373	0 6 40 64 118 120 126 138 196 208 214 216 270 294 328 334	-80505967144
SPT(14)	509500379343644033	0 36 48 50 60 86 90 116 120 146 156 158 170 206	-29798360484
SPT(14)	509500385644599499	0 22 118 154 198 204 210 232 238 244 288 324 420 442	-23497405018
SPT(14)	509500386847983731	0 12 26 30 32 62 68 90 96 126 128 132 146 158	-22294020786
TPT(12)	509500396542705719	0 2 30 32 48 50 72 74 90 92 180 182	-12599298798
SPT(14)	509500399421533589	0 14 18 24 32 38 60 62 84 90 98 104 108 122	-9720470928
SPT(14)	509500413558808033	0 36 64 66 70 84 118 126 160 174 178 180 208 244	4416803516
TPT(12)	509500430979647879	0 2 48 50 78 80 132 134 228 230 258 260	21837643362
SPT(16)	509500431960125149	0 42 88 102 108 168 192 222 250 280 304 364 370 384 430 472	22818120632
SPT(14)	509500448555102881	0 6 42 48 60 66 88 90 112 118 130 136 172 178	39413098364
SPT(14)	509500449890296069	0 52 60 64 78 118 154 168 204 244 258 262 270 322	40748291552