Prime p₀= 2048723400096253787 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 22 2 16 2 70 2 64 2 22 2 (?)
a_n: 0 2 60 62 84 86 102 104 174 176 240 242 264 266
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: 266
Found by: [SG-2W]Kurzer
db: batch=80, k=14, 58 22 16 70 64 22

SPT(16)	2048722216294587329	0 62 108 114 132 140 182 194 228 240 282 290 308 314 360 422	-1183801666458
STPT(10)	2048722528151127419	0 2 48 50 90 92 132 134 180 182	-871945126368
SPT(16)	2048722615202890447	0 30 42 52 60 120 234 276 280 322 436 496 504 514 526 556	-784893363340
SPT(16)	2048722730894860877	0 24 44 84 114 134 140 146 234 240 246 266 296 336 356 380	-669201392910
STPT(10)	2048722846058612177	0 2 24 26 42 44 60 62 84 86	-554037641610
TPT(14)	2048723059419726461	0 2 36 38 168 170 198 200 228 230 258 260 366 368	-340676527326
SPT(16)	2048723485314982759	0 12 22 24 40 70 100 114 118 132 162 192 208 210 220 232	85218728972
SPT(16)	2048723882143098959	0 32 38 54 78 128 152 170 192 210 234 284 308 324 330 362	482046845172
SPT(16)	2048723918143945219	0 22 42 64 154 160 162 214 228 280 282 288 378 400 420 442	518047691432
SPT(16)	2048724113516896873	0 70 94 144 154 168 208 214 270 276 316 330 340 390 414 484	713420643086
STPT(10)	2048724646798075451	0 2 6 8 18 20 30 32 36 38	1246701821664