Prime p₀= 36058044754811879 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 16 2 28 2 10 2 28 2 40 2 (?)
a_n: 0 2 18 20 48 50 60 62 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: Cruncher Pete
db: batch=65, k=12, 16 28 10 28 40

SPT(14)	36058019060449699	0 22 40 88 118 124 174 208 258 264 294 342 360 382	-25694362180
SPT(14)	36058021741677203	0 8 20 24 56 66 78 86 98 108 140 144 156 164	-23013134676
SPT(14)	36058022477957299	0 4 10 42 54 88 94 138 144 178 190 222 228 232	-22276854580
SPT(14)	36058036533944041	0 30 70 82 96 106 112 240 246 256 270 282 322 352	-8220867838
TPT(12)	36058041211437809	0 2 42 44 48 50 90 92 132 134 168 170	-3543374070
SPT(14)	36058042851931939	0 4 10 12 54 60 70 72 82 88 130 132 138 142	-1902879940
SPT(14)	36058049236445179	0 54 58 72 84 118 142 210 234 268 280 294 298 352	4481633300
SPT(14)	36058052187581299	0 10 22 78 84 88 108 124 144 148 154 210 222 232	7432769420
SPT(14)	36058053166284223	0 6 16 40 48 54 76 78 100 106 114 138 148 154	8411472344
SPT(14)	36058077822000209	0 20 48 54 72 84 122 180 218 230 248 254 282 302	33067188330
SPT(14)	36058105628031503	0 14 18 38 48 66 80 144 158 176 186 206 210 224	60873219624