Prime p₀= 2677215441880686977 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 166 2 28 2 10 2 58 2 76 2 (?)
a_n: 0 2 72 74 240 242 270 272 282 284 342 344 420 422
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: JayPi
db: batch=82, k=14, 70 166 28 10 58 76

SPT(16)	2677214740131234943	0 40 48 78 124 160 168 190 264 286 294 330 376 406 414 454	-701749452034
STPT(10)	2677214885503765331	0 2 6 8 48 50 90 92 96 98	-556376921646
SPT(16)	2677214893562415497	0 56 74 92 104 132 146 156 200 210 224 252 264 282 300 356	-548318271480
STPT(10)	2677215168932047229	0 2 12 14 90 92 168 170 180 182	-272948639748
TPT(14)	2677215238620095219	0 2 12 14 252 254 390 392 408 410 462 464 558 560	-203260591758
SPT(16)	2677215311174367239	0 2 30 80 90 132 170 182 288 300 338 380 390 440 468 470	-130706319738
TPT(14)	2677215973373781479	0 2 12 14 90 92 132 134 162 164 168 170 288 290	531493094502
SPT(16)	2677216630001815787	0 2 14 36 72 90 110 114 152 156 176 194 230 252 264 266	1188121128810
SPT(16)	2677217270812876391	0 12 36 56 78 110 132 138 140 146 168 200 222 242 266 278	1828932189414
STPT(10)	2677217426908216019	0 2 18 20 60 62 102 104 120 122	1985027529042
SPT(16)	2677217761648201403	0 8 48 80 84 156 158 186 188 216 218 290 294 326 366 374	2319767514426