Prime p₀= 2145269825279284127 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 118 2 106 2 22 2 76 2 40 2 (?)
a_n: 0 2 12 14 132 134 240 242 264 266 342 344 384 386
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: 386
Found by: Landjunge
db: batch=80, k=14, 10 118 106 22 76 40

SPT(16)	2145268727242957289	0 68 72 102 110 134 138 150 212 224 228 252 260 290 294 362	-1098036326838
SPT(16)	2145268812620117923	0 16 18 40 78 90 100 120 124 144 154 166 204 226 228 244	-1012659166204
STPT(10)	2145269317996446527	0 2 12 14 72 74 132 134 144 146	-507282837600
SPT(16)	2145269503559648203	0 6 24 28 66 70 78 106 138 166 174 178 216 220 238 244	-321719635924
SPT(16)	2145269575815286511	0 42 56 86 110 140 216 252 260 296 372 402 426 456 470 512	-249463997616
STPT(10)	2145269665262785739	0 2 18 20 30 32 42 44 60 62	-160016498388
TPT(14)	2145270491691072479	0 2 138 140 240 242 282 284 312 314 348 350 360 362	666411788352
SPT(16)	2145270547415958841	0 42 88 126 162 186 198 208 270 280 292 316 352 390 436 478	722136674714
TPT(14)	2145270657242371661	0 2 30 32 60 62 156 158 246 248 288 290 366 368	831963087534
SPT(16)	2145270723946019387	0 2 14 90 134 152 170 176 180 186 204 222 266 342 354 356	898666735260
SPT(16)	2145270922687547429	0 8 48 98 104 150 194 218 234 258 302 348 354 404 444 452	1097408263302