Prime p₀= 2343753006392667407 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 70 2 46 2 28 2 82 2 4 2 (?)
a_n: 0 2 30 32 102 104 150 152 180 182 264 266 270 272
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: 272
Found by: Landjunge
db: batch=81, k=14, 28 70 46 28 82 4

STPT(12)	2343752332241555531	0 2 48 50 60 62 156 158 168 170 216 218	-674151111876
STPT(10)	2343752387265426491	0 2 6 8 48 50 90 92 96 98	-619127240916
SPT(16)	2343752459670120431	0 18 32 56 60 86 98 108 140 150 162 188 192 216 230 248	-546722546976
SPT(16)	2343752594543009191	0 72 76 112 126 150 192 232 246 286 328 352 366 402 406 478	-411849658216
SPT(16)	2343752954492246081	0 26 30 32 68 96 108 116 162 170 182 210 246 248 252 278	-51900421326
SPT(16)	2343752977616586713	0 14 60 74 126 146 170 176 198 204 228 248 300 314 360 374	-28776080694
SPT(16)	2343753086845946201	0 12 48 56 60 108 110 122 126 138 140 188 192 200 236 248	80453278794
STPT(10)	2343753484377924761	0 2 6 8 18 20 30 32 36 38	477985257354
SPT(16)	2343753486486099251	0 2 20 42 72 90 156 158 210 212 278 296 326 348 366 368	480093431844
SPT(16)	2343753569635542187	0 36 70 106 112 120 126 132 160 166 172 180 186 222 256 292	563242874780
SPT(16)	2343753623159208739	0 34 42 100 108 118 168 202 300 334 384 394 402 460 468 502	616766541332