Prime p₀= 2163428645746314389 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 16 2 16 2 130 2 40 2 34 2 (?)
a_n: 0 2 42 44 60 62 78 80 210 212 252 254 288 290
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: 290
Found by: Landjunge
db: batch=81, k=14, 40 16 16 130 40 34

SPT(16)	2163427220203118773	0 10 30 40 54 70 114 150 154 190 234 250 264 274 294 304	-1425543195616
STPT(10)	2163427344509425661	0 2 6 8 18 20 30 32 36 38	-1301236888728
SPT(16)	2163427866303702307	0 64 82 84 112 214 222 256 270 304 312 414 442 444 462 526	-779442612082
STPT(12)	2163427983272652737	0 2 60 62 114 116 210 212 264 266 324 326	-662473661652
STPT(10)	2163428069539893851	0 2 36 38 78 80 120 122 156 158	-576206420538
SPT(16)	2163428591787294059	0 2 18 48 50 68 120 128 144 152 204 222 224 254 270 272	-53959020330
STPT(10)	2163428778167313791	0 2 36 38 78 80 120 122 156 158	132420999402
SPT(16)	2163428823328737407	0 44 56 66 104 132 182 282 284 384 434 462 500 510 522 566	177582423018
SPT(16)	2163429001964275979	0 8 14 24 48 104 150 198 230 278 324 380 404 414 420 428	356217961590
SPT(16)	2163429405654503867	0 20 62 72 74 84 104 110 174 180 200 210 212 222 264 284	759908189478
SPT(16)	2163429565626599947	0 4 66 132 172 174 202 250 306 354 382 384 424 490 552 556	919880285558