Prime p₀= 115358237005089851 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 34 2 28 2 22 2 34 2 130 2 (?)
a_n: 0 2 36 38 66 68 90 92 126 128 258 260
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: 260
Found by: emoga
db: batch=67, k=12, 34 28 22 34 130

SPT(14)	115358154142051543	0 66 100 106 118 150 156 238 244 276 288 294 328 394	-82863038308
SPT(14)	115358158639748509	0 70 78 90 112 114 118 144 148 150 172 184 192 262	-78365341342
TPT(12)	115358159883870359	0 2 42 44 108 110 120 122 150 152 222 224	-77121219492
TPT(12)	115358192394263477	0 2 24 26 42 44 114 116 150 152 222 224	-44610826374
SPT(14)	115358204540241307	0 12 42 72 100 102 150 172 220 222 250 280 310 322	-32464848544
SPT(14)	115358219274610957	0 12 16 24 60 64 82 84 102 106 142 150 154 166	-17730478894
SPT(14)	115358247140254483	0 4 10 18 36 120 124 150 154 238 256 264 270 274	10135164632
SPT(14)	115358254397318753	0 18 20 38 84 126 150 164 188 230 276 294 296 314	17392228902
SPT(14)	115358256356875319	0 8 78 102 132 194 222 260 288 350 380 404 474 482	19351785468
SPT(14)	115358286791681617	0 6 34 46 54 66 124 132 190 202 210 222 250 256	49786591766
SPT(14)	115358314390756121	0 32 38 62 66 86 90 98 102 122 126 150 156 188	77385666270