Prime p₀= 375294380393090231 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 106 2 58 2 40 2 4 2 82 2 (?)
a_n: 0 2 108 110 168 170 210 212 216 218 300 302
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: 302
Found by: Cruncher Pete
db: batch=70, k=12, 106 58 40 4 82

SPT(14)	375294300557385397	0 4 16 30 70 82 84 112 114 126 166 180 192 196	-79835704834
SPT(14)	375294308347123849	0 10 22 78 84 88 144 178 234 238 244 300 312 322	-72045966382
SPT(14)	375294319569718729	0 24 34 90 94 138 144 154 160 204 208 264 274 298	-60823371502
SPT(14)	375294342400357411	0 52 66 106 108 168 180 208 220 280 282 322 336 388	-37992732820
SPT(14)	375294346575699581	0 2 6 60 92 116 150 182 216 240 272 326 330 332	-33817390650
TPT(12)	375294377938438727	0 2 114 116 150 152 240 242 264 266 294 296	-2454651504
SPT(14)	375294413617943381	0 6 60 72 90 156 158 240 242 308 326 338 392 398	33224853150
SPT(16)	375294415975013869	0 12 34 52 64 124 144 258 334 448 468 528 540 558 580 592	35581923638
TPT(12)	375294443741599829	0 2 42 44 102 104 108 110 150 152 168 170	63348509598
SPT(16)	375294447524637659	0 30 44 50 74 78 84 90 128 134 140 144 168 174 188 218	67131547428
SPT(14)	375294450326192783	0 38 50 60 84 86 128 156 198 200 224 234 246 284	69933102552