Prime p₀= 2384623847620263131 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 46 2 112 2 34 2 10 2 40 2 (?)
a_n: 0 2 78 80 126 128 240 242 276 278 288 290 330 332
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: 332
Found by: Landjunge
db: batch=81, k=14, 76 46 112 34 10 40

SPT(16)	2384621524534263197	0 2 14 44 50 54 72 80 126 134 152 156 162 192 204 206	-2323085999934
STPT(10)	2384622436451987087	0 2 30 32 72 74 114 116 144 146	-1411168276044
STPT(10)	2384623046399278439	0 2 18 20 30 32 42 44 60 62	-801220984692
SPT(13)	2384623647015107119	0 30 84 114 150 168 174 180 198 234 264 318 348	-200605156012
STPT(10)	2384623688671896569	0 2 18 20 60 62 102 104 120 122	-158948366562
SPT(16)	2384623775462485157	0 6 12 20 44 54 104 144 182 222 272 282 306 314 320 326	-72157777974
SPT(16)	2384623913125430159	0 14 18 80 110 128 144 162 200 218 234 252 282 344 348 362	65505167028
TPT(14)	2384623915370257919	0 2 12 14 42 44 120 122 138 140 180 182 210 212	67749994788
STPT(10)	2384624024445270677	0 2 24 26 42 44 60 62 84 86	176825007546
SPT(16)	2384624743997567119	0 10 52 60 88 102 118 300 340 522 538 552 580 588 630 640	896377303988
STPT(10)	2384624749709691077	0 2 30 32 42 44 54 56 84 86	902089427946