Prime p₀= 2678358496118724869 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 10 2 28 2 28 2 124 2 10 2 (?)
a_n: 0 2 90 92 102 104 132 134 162 164 288 290 300 302
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: 302
Found by: [SG-2W]Kurzer
db: batch=82, k=14, 88 10 28 28 124 10

SPT(16)	2678357940506029339	0 12 34 82 84 88 90 130 132 172 174 178 180 228 250 262	-555612695530
STPT(10)	2678357940506029421	0 2 6 8 48 50 90 92 96 98	-555612695448
SPT(16)	2678358137747379433	0 30 36 64 66 76 90 108 166 184 198 208 210 238 244 274	-358371345436
STPT(10)	2678358149221916219	0 2 42 44 60 62 78 80 120 122	-346896808650
STPT(10)	2678358385692318737	0 2 42 44 72 74 102 104 144 146	-110426406132
SPT(16)	2678358391912887737	0 42 54 84 92 162 182 224 252 294 314 384 392 422 434 476	-104205837132
SPT(16)	2678358536653777057	0 36 64 66 90 126 196 222 274 300 370 406 430 432 460 496	40535052188
STPT(10)	2678358731906363027	0 2 30 32 42 44 54 56 84 86	235787638158
SPT(16)	2678359283196825791	0 2 68 78 128 180 182 192 266 276 278 330 380 390 456 458	787078100922
SPT(16)	2678359384728212329	0 4 40 42 60 112 114 148 204 238 240 292 310 312 348 352	888609487460
STPT(10)	2678359942496990417	0 2 30 32 42 44 54 56 84 86	1446378265548