Prime p₀= 2338426618771232237 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 118 2 10 2 16 2 10 2 130 2 34 2 (?)
a_n: 0 2 120 122 132 134 150 152 162 164 294 296 330 332
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, 118 10 16 10 130 34

SPT(16)	2338424748089803579	0 12 24 94 100 112 138 142 150 154 180 192 198 268 280 292	-1870681428658
STPT(10)	2338425390658126841	0 2 36 38 78 80 120 122 156 158	-1228113105396
STPT(12)	2338425653544987827	0 2 60 62 120 122 210 212 270 272 330 332	-965226244410
SPT(16)	2338426109563471463	0 8 26 54 74 120 126 128 186 188 194 240 260 288 306 314	-509207760774
STPT(12)	2338426170373286027	0 2 24 26 84 86 150 152 210 212 234 236	-448397946210
STPT(10)	2338426381652561741	0 2 30 32 78 80 126 128 156 158	-237118670496
SPT(16)	2338426949390988619	0 18 30 34 70 88 94 100 102 108 114 132 168 172 184 202	330619756382
SPT(16)	2338427054939627851	0 42 90 112 150 162 180 196 246 262 280 292 330 352 400 442	436168395614
SPT(16)	2338427187535243201	0 18 78 90 106 138 148 166 210 228 238 270 286 298 358 376	568764010964
STPT(10)	2338427345559012941	0 2 36 38 78 80 120 122 156 158	726787780704
SPT(16)	2338427367197951819	0 30 38 54 98 132 174 180 242 248 290 324 368 384 392 422	748426719582