Prime p₀= 2810553588341666267 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 28 2 40 2 28 2 28 2 34 2 (?)
a_n: 0 2 72 74 102 104 144 146 174 176 204 206 240 242
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: 242
Found by: [SG]ATA-Rolf
db: batch=82, k=14, 70 28 40 28 28 34

STPT(10)	2810551855606371971	0 2 6 8 48 50 90 92 96 98	-1732735294296
TPT(14)	2810552463872431259	0 2 18 20 42 44 48 50 78 80 90 92 102 104	-1124469235008
TPT(14)	2810553153632396477	0 2 30 32 54 56 282 284 294 296 312 314 390 392	-434709269790
SPT(16)	2810553187193019029	0 14 38 84 102 150 164 182 300 318 332 380 398 444 468 482	-401148647238
STPT(10)	2810553400841890787	0 2 30 32 72 74 114 116 144 146	-187499775480
SPT(16)	2810553496035682777	0 22 66 90 102 132 154 186 220 252 274 304 316 340 384 406	-92305983490
SPT(16)	2810553670222021379	0 8 18 108 122 144 194 210 302 318 368 390 404 494 504 512	81880355112
SPT(16)	2810554105403731619	0 50 60 62 174 182 212 234 308 330 360 368 480 482 492 542	517062065352
SPT(16)	2810554153015462489	0 4 10 34 72 132 154 160 234 240 262 322 360 384 390 394	564673796222
STPT(10)	2810554376251257677	0 2 30 32 42 44 54 56 84 86	787909591410
STPT(10)	2810555197172932199	0 2 12 14 90 92 168 170 180 182	1608831265932