Prime p₀= 115686513848183609 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 88 2 118 2 28 2 40 2 28 2 (?)
a_n: 0 2 90 92 210 212 240 242 282 284 312 314
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: 314
Found by: nenym
db: batch=67, k=12, 88 118 28 40 28

SPT(14)	115686446672854951	0 66 82 88 90 126 132 256 262 298 300 306 322 388	-67175328658
TPT(12)	115686449941689071	0 2 90 92 126 128 156 158 198 200 210 212	-63906494538
TPT(12)	115686462630750797	0 2 30 32 60 62 90 92 144 146 162 164	-51217432812
SPT(14)	115686473339002103	0 26 44 180 200 264 270 290 296 360 380 516 534 560	-40509181506
SPT(14)	115686474317394637	0 10 16 30 54 70 82 114 126 142 166 180 186 196	-39530788972
SPT(14)	115686476879005367	0 14 44 56 140 164 170 186 192 216 300 312 342 356	-36969178242
SPT(14)	115686519093190889	0 2 62 74 78 90 120 152 182 194 198 210 270 272	5245007280
SPT(14)	115686547429219717	0 10 52 54 60 70 84 100 114 124 130 132 174 184	33581036108
SPT(14)	115686550030199237	0 26 50 60 116 152 192 194 234 270 326 336 360 386	36182015628
SPT(14)	115686558890007319	0 40 88 100 114 142 168 184 210 238 252 264 312 352	45041823710
SPT(14)	115686560529110381	0 6 20 32 42 68 150 188 270 296 306 318 332 338	46680926772