Prime p₀= 353719541276409767 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 112 2 16 2 106 2 10 2 58 2 (?)
a_n: 0 2 114 116 132 134 240 242 252 254 312 314
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: desktop64
db: batch=70, k=12, 112 16 106 10 58

TPT(12)	353719494381954641	0 2 78 80 90 92 96 98 150 152 210 212	-46894455126
SPT(14)	353719505268091033	0 10 96 100 114 154 156 178 180 220 234 238 324 334	-36008318734
SPT(14)	353719510938713971	0 18 28 46 60 78 100 198 220 238 252 270 280 298	-30337695796
SPT(14)	353719514383480771	0 18 22 42 60 100 126 142 168 208 226 246 250 268	-26892928996
SPT(14)	353719528913166467	0 32 102 146 150 156 174 242 260 266 270 314 384 416	-12363243300
SPT(14)	353719535942319149	0 12 14 32 72 80 102 122 144 152 192 210 212 224	-5334090618
SPT(14)	353719551438995699	0 18 24 132 138 140 152 180 192 194 200 308 314 332	10162585932
SPT(14)	353719578580674653	0 48 50 128 140 156 168 188 200 216 228 306 308 356	37304264886
SPT(14)	353719591996292281	0 16 18 60 78 100 118 198 216 238 256 298 300 316	50719882514
TPT(12)	353719599762540797	0 2 84 86 144 146 162 164 240 242 294 296	58486131030
TPT(12)	353719609186054127	0 2 30 32 42 44 84 86 120 122 144 146	67909644360