Prime p₀= 253165028626409969 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 16 2 40 2 106 2 10 2 58 2 (?)
a_n: 0 2 18 20 60 62 168 170 180 182 240 242
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: 242
Found by: desktop64
db: batch=69, k=12, 16 40 106 10 58

SPT(14)	253164976659286123	0 4 6 54 60 84 94 120 130 154 160 208 210 214	-51967123846
SPT(14)	253164997358387899	0 30 42 58 78 82 114 148 180 184 204 220 232 262	-31268022070
SPT(14)	253165005377009963	0 30 48 80 90 98 108 146 156 164 174 206 224 254	-23249400006
SPT(14)	253165009092290237	0 12 42 54 60 92 104 180 192 224 230 242 272 284	-19534119732
SPT(14)	253165019573865481	0 10 70 106 108 112 162 166 216 220 222 258 318 328	-9052544488
TPT(12)	253165021630123037	0 2 12 14 30 32 54 56 162 164 204 206	-6996286932
SPT(14)	253165038616011827	0 12 54 74 104 140 152 174 186 222 252 272 314 326	9989601858
SPT(16)	253165039935685411	0 18 78 88 112 130 150 162 178 190 210 228 252 262 322 340	11309275442
SPT(14)	253165052679568219	0 40 42 72 82 94 112 150 168 180 190 220 222 262	24053158250
SPT(14)	253165058422179601	0 12 46 48 70 76 102 196 222 228 250 252 286 298	29795769632
SPT(14)	253165101486318199	0 34 58 118 168 178 198 304 324 334 384 444 468 502	72859908230