Prime p₀= 323615253316031309 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 40 2 4 2 40 2 46 2 40 2 (?)
a_n: 0 2 42 44 48 50 90 92 138 140 180 182
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: 182
Found by: desktop64
db: batch=70, k=12, 40 4 40 46 40

SPT(14)	323615158795448161	0 28 70 126 162 166 178 180 192 196 232 288 330 358	-94520583148
SPT(14)	323615170349104619	0 14 24 42 72 90 102 152 164 182 212 230 240 254	-82966926690
SPT(14)	323615193489683897	0 32 42 62 84 114 132 152 170 200 222 242 252 284	-59826347412
SPT(14)	323615226092888711	0 20 50 62 66 78 98 210 230 242 246 258 288 308	-27223142598
SPT(14)	323615230848208361	0 6 20 32 152 188 228 350 390 426 546 558 572 578	-22467822948
SPT(14)	323615247755762947	0 6 10 34 46 96 124 216 244 294 306 330 334 340	-5560268362
SPT(14)	323615257869041599	0 40 42 52 130 138 142 168 172 180 258 268 270 310	4553010290
TPT(12)	323615290772293151	0 2 30 32 36 38 60 62 186 188 210 212	37456261842
SPT(16)	323615313317027569	0 4 10 34 40 54 60 78 94 112 118 132 138 162 168 172	60000996260
SPT(14)	323615355286866121	0 6 22 30 96 120 142 180 202 226 292 300 316 322	101970834812
SPT(16)	323615364353410099	0 22 48 70 78 102 120 132 190 202 220 244 252 274 300 322	111037378790