Prime p₀= 2577540458800165097 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 124 2 28 2 40 2 28 2 166 2 (?)
a_n: 0 2 24 26 150 152 180 182 222 224 252 254 420 422
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: [SG-2W]Kurzer
db: batch=82, k=14, 22 124 28 40 28 166

TPT(14)	2577539665353824291	0 2 156 158 168 170 180 182 330 332 420 422 456 458	-793446340806
SPT(16)	2577539707720823371	0 36 40 52 70 96 166 172 246 252 322 348 366 378 382 418	-751079341726
SPT(16)	2577539774237721707	0 14 24 50 56 60 134 150 170 186 260 264 270 296 306 320	-684562443390
STPT(10)	2577539778505338089	0 2 18 20 60 62 102 104 120 122	-680294827008
TPT(14)	2577539930185881719	0 2 48 50 78 80 90 92 102 104 240 242 258 260	-528614283378
SPT(16)	2577540207102925957	0 34 96 154 156 166 180 184 282 286 300 310 312 370 432 466	-251697239140
STPT(12)	2577540534706046249	0 2 60 62 90 92 138 140 168 170 228 230	75905881152
TPT(14)	2577542314862571071	0 2 36 38 78 80 96 98 246 248 318 320 378 380	1856062405974
SPT(16)	2577542440763762497	0 12 16 46 54 82 90 126 130 166 174 202 210 240 244 256	1981963597400
SPT(16)	2577542628993217133	0 6 24 30 54 110 114 134 210 230 234 290 314 320 338 344	2170193052036
STPT(10)	2577542728937247077	0 2 30 32 42 44 54 56 84 86	2270137081980