Prime p₀= 1572096331350746231 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 88 2 118 2 16 2 28 2 46 2 (?)
a_n: 0 2 30 32 120 122 240 242 258 260 288 290 336 338
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: 338
Found by: [SG-2W]Kurzer
db: batch=78, k=14, 28 88 118 16 28 46

SPT(16)	1572095564670202393	0 40 48 54 100 108 150 174 184 208 250 258 304 310 318 358	-766680543838
STPT(10)	1572095664526882667	0 2 30 32 42 44 54 56 84 86	-666823863564
TPT(14)	1572095855799088481	0 2 78 80 96 98 108 110 120 122 156 158 198 200	-475551657750
STPT(10)	1572096097714808591	0 2 30 32 78 80 126 128 156 158	-233635937640
SPT(16)	1572096291940026847	0 10 12 70 120 144 180 184 192 196 232 256 306 364 366 376	-39410719384
SPT(16)	1572096295363175213	0 36 48 66 84 114 168 186 188 206 260 290 308 326 338 374	-35987571018
STPT(10)	1572096553220537117	0 2 54 56 72 74 90 92 144 146	221869790886
SPT(16)	1572096604201383031	0 22 46 48 66 118 132 150 238 256 270 322 340 342 366 388	272850636800
SPT(16)	1572096811178726741	0 2 6 32 42 60 98 126 212 240 278 296 306 332 336 338	479827980510
STPT(10)	1572096884968524329	0 2 48 50 60 62 72 74 120 122	553617778098
SPT(16)	1572097044158171233	0 16 36 40 48 96 118 120 154 156 178 226 234 238 258 274	712807425002