Prime p₀= 768009259481180711 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 28 2 10 2 280 2 28 2 16 2 (?)
a_n: 0 2 36 38 66 68 78 80 360 362 390 392 408 410
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 410
Found by: gemini8
db: batch=73, k=14, 34 28 10 280 28 16

TPT(18)	768007934690823551	0 2 30 32 48 50 60 62 180 182 228 230 240 242 336 338 366 368	-1324790357160
STPT(10)	768008109537460637	0 2 24 26 42 44 60 62 84 86	-1149943720074
TPT(14)	768008234203648937	0 2 30 32 42 44 144 146 174 176 210 212 252 254	-1025277531774
SPT(16)	768008344351908001	0 18 28 52 88 90 102 108 112 118 130 132 168 192 202 220	-915129272710
TPT(14)	768008721477936941	0 2 6 8 60 62 168 170 210 212 246 248 288 290	-538003243770
STPT(10)	768009005506965107	0 2 12 14 72 74 132 134 144 146	-253974215604
SPT(16)	768009291463923277	0 10 30 40 42 52 70 94 132 156 174 184 186 196 216 226	31982742566
SPT(16)	768009357240703219	0 10 48 82 94 124 148 180 232 264 288 318 330 364 402 412	97759522508
SPT(16)	768009630228423403	0 16 30 100 106 108 118 126 178 186 196 198 204 274 288 304	370747242692
SPT(16)	768009973953011617	0 6 34 70 90 100 114 154 156 196 210 220 240 276 304 310	714471830906
SPT(16)	768010222578887713	0 18 28 40 64 90 120 144 154 178 208 234 258 270 280 298	963097707002