Prime p₀= 144303056960957759 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 16 2 82 2 106 2 16 2 22 2 (?)
a_n: 0 2 18 20 102 104 210 212 228 230 252 254
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: 254
Found by: emoga
db: batch=67, k=12, 16 82 106 16 22

SPT(14)	144303011639528239	0 4 10 18 24 40 42 70 72 88 94 102 108 112	-45321429520
SPT(14)	144303017373268499	0 14 74 78 102 120 128 144 152 170 194 198 258 272	-39587689260
SPT(14)	144303018878363273	0 36 60 68 120 140 146 180 186 206 258 266 290 326	-38082594486
TPT(12)	144303024197364677	0 2 150 152 162 164 192 194 204 206 210 212	-32763593082
STPT(10)	144303034357696811	0 2 36 38 78 80 120 122 156 158	-22603260948
SPT(14)	144303046171516931	0 2 20 56 80 132 152 210 230 282 306 342 360 362	-10789440828
SPT(14)	144303060214189397	0 42 54 114 140 162 212 264 314 336 362 422 434 476	3253231638
SPT(14)	144303069386773019	0 24 42 50 90 150 182 240 272 332 372 380 398 422	12425815260
SPT(14)	144303070364555251	0 36 58 78 88 120 130 168 178 210 220 240 262 298	13403597492
SPT(14)	144303088211337551	0 6 12 80 138 146 182 276 312 320 378 446 452 458	31250379792
SPT(16)	144303097439397679	0 70 90 112 154 172 180 222 292 334 342 360 402 424 444 514	40478439920