Prime p₀= 2337082451761632719 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 10 2 28 2 106 2 28 2 58 2 (?)
a_n: 0 2 60 62 72 74 102 104 210 212 240 242 300 302
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: 302
Found by: Landjunge
db: batch=81, k=14, 58 10 28 106 28 58

SPT(16)	2337081227158158601	0 96 120 136 148 168 178 180 196 198 208 228 240 256 280 376	-1224603474118
SPT(16)	2337081248328038183	0 26 60 66 98 156 158 168 296 306 308 366 398 404 438 464	-1203433594536
SPT(16)	2337081579693785263	0 10 124 150 166 210 240 250 264 274 304 348 364 390 504 514	-872067847456
SPT(16)	2337081681330509849	0 140 152 162 194 222 264 284 288 308 350 378 410 420 432 572	-770431122870
STPT(10)	2337081959143456709	0 2 30 32 60 62 90 92 120 122	-492618176010
STPT(12)	2337082421270372957	0 2 24 26 30 32 54 56 60 62 84 86	-30491259762
TPT(14)	2337082786493293247	0 2 162 164 180 182 210 212 234 236 264 266 300 302	334731660528
SPT(16)	2337083063261967947	0 36 54 84 174 176 222 264 302 344 390 392 482 512 530 566	611500335228
TPT(14)	2337083272395179879	0 2 18 20 48 50 72 74 102 104 138 140 228 230	820633547160
STPT(10)	2337083294360670641	0 2 36 38 78 80 120 122 156 158	842599037922
SPT(16)	2337083472480632927	0 2 32 50 56 60 80 102 140 162 182 186 192 210 240 242	1020719000208