Prime p₀= 1081039718201839241 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 16 2 40 2 4 2 40 2 16 2 (?)
a_n: 0 2 18 20 60 62 66 68 108 110 126 128
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: 128
Found by: Theadalus
db: batch=76, k=12, 2 16 2 40 2 4

STPT(10)	1081038646686791657	0 2 42 44 72 74 102 104 144 146	-1071515047584
SPT(16)	1081038966784490617	0 30 36 82 112 124 154 166 210 222 252 264 294 340 346 376	-751417348624
SPT(16)	1081038968303206061	0 32 42 80 86 116 120 168 290 338 342 372 378 416 426 458	-749898633180
STPT(10)	1081039035102096839	0 2 18 20 30 32 42 44 60 62	-683099742402
SPT(16)	1081039097514986531	0 32 38 56 62 126 152 176 192 216 242 306 312 330 336 368	-620686852710
SPT(16)	1081039250055034819	0 24 30 48 82 142 178 190 252 264 300 360 394 412 418 442	-468146804422
SPT(16)	1081039734853173479	0 18 38 42 74 80 98 104 108 114 132 138 170 174 194 212	16651334238
SPT(16)	1081039777432614877	0 12 16 30 52 70 100 150 166 216 246 264 286 300 304 316	59230775636
TPT(14)	1081040028737535047	0 2 24 26 42 44 150 152 234 236 240 242 264 266	310535695806
SPT(18)	1081040034788025539	0 2 14 62 68 128 140 152 174 188 210 222 234 294 300 348 360 362	316586186298
SPT(16)	1081040125095870697	0 6 30 60 66 94 132 156 190 214 252 280 286 316 340 346	406894031456