Prime p₀= 2167242879544376657 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 82 2 34 2 28 2 28 2 40 2 (?)
a_n: 0 2 90 92 174 176 210 212 240 242 270 272 312 314
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: 314
Found by: Penguin
db: batch=81, k=14, 88 82 34 28 28 40

SPT(16)	2167241456948011453	0 58 78 106 126 130 154 246 268 360 384 388 408 436 456 514	-1422596365204
SPT(16)	2167241701839428189	0 2 20 42 68 110 132 180 182 230 252 294 320 342 360 362	-1177704948468
SPT(16)	2167242050006646643	0 76 78 118 174 240 258 274 330 346 364 430 486 526 528 604	-829537730014
SPT(16)	2167242075286336067	0 12 24 50 66 84 110 144 182 216 242 260 276 302 314 326	-804258040590
SPT(16)	2167242085609108843	0 10 34 46 66 96 124 136 294 306 334 364 384 396 420 430	-793935267814
SPT(16)	2167242261953218171	0 10 16 18 30 40 60 88 150 178 198 208 220 222 228 238	-617591158486
SPT(20)	2167243263346446517	0 22 24 46 60 72 94 130 144 156 220 232 246 282 304 316 330 352 354 376	383802069860
STPT(10)	2167243281945089981	0 2 6 8 48 50 90 92 96 98	402400713324
SPT(16)	2167243469035901467	0 52 70 72 94 100 102 120 136 154 156 162 184 186 204 256	589491524810
STPT(10)	2167243644513608357	0 2 12 14 72 74 132 134 144 146	764969231700
SPT(16)	2167244069904491093	0 20 38 60 80 104 116 200 234 318 330 354 374 396 414 434	1190360114436