Prime p₀= 2319692613290260601 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 118 2 4 2 82 2 64 2 112 2 (?)
a_n: 0 2 30 32 150 152 156 158 240 242 306 308 420 422
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: 422
Found by: Landjunge
db: batch=81, k=14, 28 118 4 82 64 112

SPT(16)	2319691443067799039	0 38 68 98 108 120 194 228 284 318 392 404 414 444 474 512	-1170222461562
STPT(10)	2319691770806617301	0 2 6 8 48 50 90 92 96 98	-842483643300
STPT(10)	2319691895041507121	0 2 36 38 78 80 120 122 156 158	-718248753480
STPT(10)	2319692257074524117	0 2 30 32 60 62 90 92 120 122	-356215736484
SPT(16)	2319692515664264333	0 8 26 38 98 108 140 150 176 186 218 228 288 300 318 326	-97625996268
TPT(14)	2319692580171482387	0 2 60 62 180 182 264 266 300 302 342 344 384 386	-33118778214
SPT(16)	2319692644771553833	0 18 60 88 126 144 168 174 190 196 220 238 276 304 346 364	31481293232
SPT(16)	2319693022739022191	0 30 62 66 72 86 98 108 140 150 162 176 182 186 218 248	409448761590
SPT(16)	2319693154760176529	0 54 80 120 144 174 182 224 228 270 278 308 332 372 398 452	541469915928
SPT(16)	2319693250106384989	0 18 30 58 100 114 124 174 238 288 298 312 354 382 394 412	636816124388
STPT(10)	2319693341657579969	0 2 12 14 90 92 168 170 180 182	728367319368