Prime p₀= 125518995868191719 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 118 2 10 2 4 2 22 2 16 2 (?)
a_n: 0 2 120 122 132 134 138 140 162 164 180 182
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: cpuid
db: batch=67, k=12, 118 10 4 22 16

SPT(14)	125518921922019757	0 6 10 42 96 120 150 316 346 370 424 456 460 466	-73946171962
SPT(14)	125518924089259451	0 48 90 170 182 192 200 240 248 258 270 350 392 440	-71778932268
SPT(14)	125518937584393277	0 72 84 134 152 210 224 240 254 312 330 380 392 464	-58283798442
SPT(14)	125518963838244371	0 38 42 62 72 90 108 110 128 146 156 176 180 218	-32029947348
TPT(12)	125518972414835771	0 2 48 50 90 92 120 122 156 158 186 188	-23453355948
SPT(16)	125518977566802517	0 12 76 96 102 120 154 166 210 222 256 274 280 300 364 376	-18301389202
TPT(12)	125518996574338019	0 2 30 32 42 44 48 50 78 80 90 92	706146300
SPT(14)	125519026852021687	0 66 76 96 210 274 276 304 306 370 484 504 514 580	30983829968
SPT(14)	125519039057581903	0 34 60 88 96 118 126 178 186 208 216 244 270 304	43189390184
SPT(14)	125519049978008383	0 46 78 88 90 124 126 208 210 244 246 256 288 334	54109816664
SPT(14)	125519068276247761	0 40 70 82 168 178 192 208 222 232 318 330 360 400	72408056042