Prime p₀= 41658566543694209 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 28 2 10 2 28 2 16 2 40 2 (?)
a_n: 0 2 30 32 42 44 72 74 90 92 132 134
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: 134
Found by: pelpolaris
db: batch=65, k=12, 28 10 28 16 40

SPT(14)	41658521757747701	0 2 42 50 60 78 98 192 212 230 240 248 288 290	-44785946508
SPT(14)	41658529065272611	0 18 22 48 52 78 88 90 100 126 130 156 160 178	-37478421598
SPT(14)	41658546578522141	0 36 48 56 72 92 102 116 126 146 162 170 182 218	-19965172068
SPT(14)	41658546763370389	0 4 10 24 28 40 52 90 102 114 118 132 138 142	-19780323820
SPT(14)	41658558141498461	0 18 30 78 80 98 120 128 150 168 170 218 230 248	-8402195748
SPT(16)	41658561953200403	0 18 24 38 44 56 60 96 98 134 138 150 156 170 176 194	-4590493806
SPT(14)	41658568065735833	0 14 38 44 66 78 98 156 176 188 210 216 240 254	1522041624
SPT(14)	41658575264666993	0 44 50 78 80 90 114 140 164 174 176 204 210 254	8720972784
SPT(14)	41658579890502703	0 10 16 30 58 100 118 126 144 186 214 228 234 244	13346808494
TPT(12)	41658586895273279	0 2 180 182 198 200 222 224 318 320 348 350	20351579070
SPT(14)	41658589951237309	0 18 22 30 42 58 84 88 114 130 142 150 154 172	23407543100