Prime p₀= 2351535263058673331 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 40 2 16 2 10 2 40 2 4 2 (?)
a_n: 0 2 6 8 48 50 66 68 78 80 120 122 126 128
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: 128
Found by: [SG-2W]Kurzer
db: batch=81, k=14, 4 40 16 10 40 4

SPT(18)	2351533136914169599	0 4 30 70 72 114 130 138 154 228 244 252 268 310 312 352 378 382	-2126144503732
STPT(12)	2351533590886082789	0 2 90 92 102 104 168 170 180 182 270 272	-1672172590542
STPT(10)	2351533802967460157	0 2 54 56 72 74 90 92 144 146	-1460091213174
STPT(10)	2351534245699707329	0 2 48 50 60 62 72 74 120 122	-1017358966002
STPT(10)	2351534921857221797	0 2 12 14 72 74 132 134 144 146	-341201451534
SPT(16)	2351535032630560199	0 44 62 90 164 194 222 260 294 332 360 390 464 492 510 554	-230428113132
SPT(16)	2351535400603619033	0 66 74 86 96 108 168 180 254 266 326 338 348 360 368 434	137544945702
SPT(16)	2351535420986027621	0 20 38 42 78 80 90 108 140 158 168 170 206 210 228 248	157927354290
STPT(10)	2351535926814112037	0 2 24 26 42 44 60 62 84 86	663755438706
STPT(10)	2351535985449496631	0 2 30 32 78 80 126 128 156 158	722390823300
SPT(16)	2351536166704094093	0 8 78 98 138 174 204 210 224 230 260 296 336 356 426 434	903645420762