Prime p₀= 2158027837726856237 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 10 2 28 2 58 2 28 2 76 2 (?)
a_n: 0 2 72 74 84 86 114 116 174 176 204 206 282 284
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: 284
Found by: Landjunge
db: batch=81, k=14, 70 10 28 58 28 76

SPT(16)	2158026009467299483	0 24 40 46 64 66 228 238 246 256 418 420 438 444 460 484	-1828259556754
TPT(14)	2158026119467862297	0 2 24 26 54 56 90 92 210 212 234 236 330 332	-1718258993940
STPT(10)	2158026649064373359	0 2 18 20 30 32 42 44 60 62	-1188662482878
STPT(10)	2158027092265311611	0 2 36 38 78 80 120 122 156 158	-745461544626
STPT(10)	2158027341177565139	0 2 18 20 60 62 102 104 120 122	-496549291098
TPT(14)	2158027818299219441	0 2 66 68 150 152 156 158 276 278 390 392 408 410	-19427636796
SPT(16)	2158028298117877931	0 32 50 98 102 140 152 168 212 228 240 278 282 330 348 380	460391021694
STPT(12)	2158028428416712979	0 2 12 14 72 74 78 80 138 140 150 152	590689856742
SPT(16)	2158028547900736897	0 70 94 100 150 156 184 214 246 276 304 310 360 366 390 460	710173880660
STPT(10)	2158028572415139791	0 2 6 8 48 50 90 92 96 98	734688283554
SPT(16)	2158028623555415239	0 82 88 94 114 142 144 150 202 208 210 238 258 264 270 352	785828559002