Prime p₀= 2134594165916296919 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 28 2 22 2 16 2 10 2 28 2 (?)
a_n: 0 2 18 20 48 50 72 74 90 92 102 104 132 134
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: 134
Found by: Landjunge
db: batch=80, k=14, 16 28 22 16 10 28

SPT(16)	2134592169379130509	0 52 102 124 130 142 154 180 184 210 222 234 240 262 312 364	-1996537166410
SPT(16)	2134592502032694653	0 54 78 80 96 98 120 126 158 164 186 188 204 206 230 284	-1663883602266
SPT(16)	2134592568876918191	0 38 56 66 90 96 98 122 126 150 152 158 182 192 210 248	-1597039378728
STPT(10)	2134592627782907597	0 2 30 32 42 44 54 56 84 86	-1538133389322
SPT(16)	2134593293351992871	0 12 68 72 90 110 126 158 180 212 228 248 266 270 326 338	-872564304048
STPT(10)	2134593581006766359	0 2 18 20 30 32 42 44 60 62	-584909530560
SPT(16)	2134594533743499871	0 16 36 60 66 70 72 88 120 136 138 142 148 172 192 208	367827202952
STPT(10)	2134594546386726077	0 2 54 56 132 134 210 212 264 266	380470429158
SPT(16)	2134594562521831117	0 22 24 52 60 82 130 142 234 246 294 316 324 352 354 376	396605534198
STPT(10)	2134594597089495377	0 2 42 44 72 74 102 104 144 146	431173198458
SPT(16)	2134595196071216713	0 6 16 30 126 136 168 246 268 346 378 388 484 498 508 514	1030154919794