Prime p₀= 2576807755048298687 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 40 2 58 2 34 2 28 2 70 2 (?)
a_n: 0 2 42 44 84 86 144 146 180 182 210 212 282 284
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: 284
Found by: [SG]ATA-Rolf
db: batch=82, k=14, 40 40 58 34 28 70

SPT(16)	2576805945574337483	0 30 74 108 144 168 188 248 276 336 356 380 416 450 494 524	-1809473961204
SPT(16)	2576806080612553061	0 20 30 56 86 90 96 132 230 266 272 276 306 332 342 362	-1674435745626
SPT(16)	2576806159162965683	0 24 38 84 90 116 150 254 330 434 468 494 500 546 560 584	-1595885333004
STPT(10)	2576806731070782011	0 2 6 8 48 50 90 92 96 98	-1023977516676
SPT(16)	2576807120853987289	0 28 30 42 48 64 90 102 130 142 168 184 190 202 204 232	-634194311398
SPT(16)	2576807547683016173	0 18 56 78 144 164 180 198 206 224 240 260 326 348 386 404	-207365282514
STPT(12)	2576807804351933939	0 2 12 14 42 44 48 50 78 80 90 92	49303635252
SPT(16)	2576808168907019057	0 6 14 20 26 36 50 86 180 216 230 240 246 252 260 266	413858720370
STPT(10)	2576808254264944727	0 2 30 32 42 44 54 56 84 86	499216646040
SPT(16)	2576808348838548841	0 16 42 46 48 60 156 178 210 232 328 340 342 346 372 388	593790250154
STPT(10)	2576808420386152571	0 2 90 92 150 152 210 212 300 302	665337853884