Prime p₀= 11558583437374409 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 100 2 28 2 34 2 88 2 22 2 (?)
a_n: 0 2 102 104 132 134 168 170 258 260 282 284
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: 284
Found by: UBT - Timbo
db: batch=62, k=12, 100 28 34 88 22

SPT(14)	11558554650340457	0 2 6 12 30 42 62 84 104 116 134 140 144 146	-28787033952
SPT(14)	11558570799152851	0 6 36 60 66 106 108 190 192 232 238 262 292 298	-12638221558
SPT(14)	11558570941313761	0 58 60 72 78 148 162 346 360 430 436 448 450 508	-12496060648
SPT(14)	11558571142160257	0 76 102 112 120 144 154 222 232 256 264 274 300 376	-12295214152
SPT(14)	11558578136842483	0 40 48 60 108 154 244 264 354 400 448 460 468 508	-5300531926
TPT(12)	11558581119341897	0 2 54 56 84 86 144 146 312 314 324 326	-2318032512
SPT(14)	11558597911362809	0 14 32 42 54 60 62 150 152 158 170 180 198 212	14473988400
SPT(14)	11558603072452039	0 24 42 84 108 114 130 132 148 154 178 220 238 262	19635077630
SPT(14)	11558605948344071	0 12 38 42 60 108 116 162 170 218 236 240 266 278	22510969662
SPT(14)	11558611584820753	0 48 66 70 76 90 96 118 124 138 144 148 166 214	28147446344
SPT(14)	11558616926335433	0 6 8 26 30 54 86 138 170 194 198 216 218 224	33488961024