Prime p₀= 27628788033503051 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 64 2 28 2 52 2 106 2 40 2 (?)
a_n: 0 2 66 68 96 98 150 152 258 260 300 302
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: 302
Found by: UBT - Timbo
db: batch=65, k=12, 64 28 52 106 40

SPT(14)	27628746424338721	0 36 46 120 148 166 168 208 210 228 256 330 340 376	-41609164330
TPT(12)	27628762555502861	0 2 126 128 198 200 210 212 228 230 240 242	-25478000190
SPT(14)	27628763093242387	0 16 24 70 76 90 136 234 280 294 300 346 354 370	-24940260664
SPT(14)	27628767630146261	0 8 36 42 78 80 102 116 138 140 176 182 210 218	-20403356790
SPT(14)	27628775403025123	0 6 18 60 84 96 108 196 208 220 244 286 298 304	-12630477928
SPT(14)	27628785657977671	0 12 70 72 76 90 126 172 208 222 226 228 286 298	-2375525380
SPT(14)	27628790666424289	0 34 40 42 70 94 112 150 168 192 220 222 228 262	2632921238
SPT(14)	27628791473852017	0 12 36 42 60 66 72 94 100 106 124 130 154 166	3440348966
SPT(14)	27628808808271661	0 6 26 42 50 60 72 116 128 138 146 162 182 188	20774768610
SPT(14)	27628808966724107	0 20 24 32 60 74 102 104 132 146 174 182 186 206	20933221056
SPT(14)	27628812196227647	0 26 32 54 72 84 122 174 212 224 242 264 270 296	24162724596