Prime p₀= 341476376736549737 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 10 2 76 2 10 2 10 2 64 2 (?)
a_n: 0 2 12 14 90 92 102 104 114 116 180 182
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: Cruncher Pete
db: batch=70, k=12, 10 76 10 10 64

SPT(14)	341476301996490979	0 10 28 52 82 90 108 142 160 168 198 222 240 250	-74740058758
SPT(14)	341476317143091661	0 12 42 48 66 76 88 90 102 112 130 136 166 178	-59593458076
TPT(12)	341476322714536949	0 2 18 20 78 80 102 104 120 122 162 164	-54022012788
SPT(14)	341476337694977477	0 80 84 116 150 170 186 194 210 230 264 296 300 380	-39041572260
SPT(14)	341476353287909969	0 30 42 108 134 182 198 224 240 288 314 380 392 422	-23448639768
SPT(14)	341476374413147257	0 16 60 70 82 84 102 154 172 174 186 196 240 256	-2323402480
SPT(14)	341476395579710509	0 10 28 48 70 100 112 138 150 180 202 222 240 250	18843160772
SPT(14)	341476415674804181	0 2 36 38 50 56 62 66 72 78 90 92 126 128	38938254444
SPT(14)	341476433221095779	0 32 48 78 98 102 104 138 140 144 164 194 210 242	56484546042
SPT(14)	341476435311357631	0 48 88 102 120 148 168 172 192 220 238 252 292 340	58574807894
SPT(14)	341476485513057617	0 20 32 56 72 84 86 90 92 104 120 144 156 176	108776507880