Prime p₀= 3034568365906626881 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 58 2 28 2 40 2 76 2 10 2 (?)
a_n: 0 2 36 38 96 98 126 128 168 170 246 248 258 260
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: 260
Found by: [SG]ATA-Rolf
db: batch=82, k=14, 34 58 28 40 76 10

SPT(16)	3034567392606228923	0 14 30 38 48 114 126 164 240 278 290 356 366 374 390 404	-973300397958
TPT(14)	3034567542547361057	0 2 24 26 54 56 84 86 150 152 240 242 354 356	-823359265824
SPT(18)	3034567907122382377	0 40 60 64 70 82 90 130 160 174 204 244 252 264 270 274 294 334	-458784244504
SPT(20)	3034567912229817707	0 14 30 74 84 86 102 132 176 182 234 240 284 314 330 332 342 386 402 416	-453676809174
SPT(16)	3034568103119053219	0 10 60 64 88 118 124 144 364 384 390 420 444 448 498 508	-262787573662
STPT(10)	3034568242617995519	0 2 42 44 60 62 78 80 120 122	-123288631362
SPT(16)	3034568540344609897	0 16 24 52 54 84 154 172 234 252 322 352 354 382 390 406	174437983016
STPT(10)	3034568577913432529	0 2 12 14 30 32 48 50 60 62	212006805648
SPT(16)	3034568632353742837	0 22 70 82 90 94 160 166 360 366 432 436 444 456 504 526	266447115956
SPT(16)	3034568675027813639	0 24 30 48 132 144 158 162 170 174 188 200 284 302 308 332	309121186758
SPT(16)	3034568785076298521	0 32 50 62 86 150 162 198 260 296 308 372 396 408 426 458	419169671640