Prime p₀= 2729503019346860717 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 112 2 16 2 40 2 76 2 16 2 22 2 (?)
a_n: 0 2 114 116 132 134 174 176 252 254 270 272 294 296
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: 296
Found by: JayPi
db: batch=82, k=14, 112 16 40 76 16 22

SPT(16)	2729501817991916687	0 2 14 20 42 44 62 110 144 192 210 212 234 240 252 254	-1201354944030
TPT(14)	2729501879934288461	0 2 30 32 36 38 60 62 78 80 120 122 228 230	-1139412572256
SPT(16)	2729502089982365773	0 10 40 70 84 150 160 168 220 228 238 304 318 348 378 388	-929364494944
SPT(16)	2729502649883827819	0 18 28 40 42 154 180 198 364 382 408 520 522 534 544 562	-369463032898
SPT(16)	2729502697465107871	0 28 40 66 88 118 126 160 228 262 270 300 322 348 360 388	-321881752846
SPT(16)	2729502961081020353	0 6 54 56 98 110 116 146 228 258 264 276 318 320 368 374	-58265840364
SPT(16)	2729503148068370677	0 12 22 42 76 82 100 112 120 132 150 156 190 210 220 232	128721509960
SPT(16)	2729503304280567149	0 2 18 24 48 60 80 102 110 132 152 164 188 194 210 212	284933706432
TPT(14)	2729503447639089827	0 2 24 26 30 32 54 56 144 146 192 194 270 272	428292229110
SPT(16)	2729503790840536711	0 36 40 42 72 78 108 138 250 280 310 316 346 348 352 388	771493675994
SPT(16)	2729503859936936317	0 6 16 34 36 70 160 186 214 240 330 364 366 384 394 400	840590075600