Prime p₀= 2727575887256467979 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 16 2 148 2 28 2 28 2 100 2 (?)
a_n: 0 2 12 14 30 32 180 182 210 212 240 242 342 344
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: 344
Found by: JayPi
db: batch=82, k=14, 10 16 148 28 28 100

SPT(16)	2727575314207578253	0 6 48 70 118 124 160 178 336 354 390 396 444 466 508 514	-573048889726
SPT(16)	2727575322904342597	0 10 16 22 30 64 70 82 84 96 102 136 144 150 156 166	-564352125382
SPT(16)	2727575537452600397	0 14 24 30 176 194 234 266 330 362 402 420 566 572 582 596	-349803867582
SPT(16)	2727575699066741581	0 28 42 76 102 108 112 160 168 216 220 226 252 286 300 328	-188189726398
SPT(16)	2727575754114232123	0 6 18 40 64 76 78 90 154 166 168 180 204 226 238 244	-133142235856
STPT(10)	2727575792589408749	0 2 18 20 30 32 42 44 60 62	-94667059230
SPT(16)	2727575889298807177	0 12 24 102 120 124 126 142 234 250 252 256 274 352 364 376	2042339198
SPT(16)	2727575990411093683	0 30 54 64 166 180 184 190 270 276 280 294 396 406 430 460	103154625704
SPT(16)	2727576142083888607	0 24 100 102 130 136 166 172 204 210 240 246 274 276 352 376	254827420628
SPT(20)	2727576158079177127	0 60 64 100 130 136 154 162 196 262 294 360 394 402 420 426 456 492 496 556	270822709148
SPT(16)	2727576307433808913	0 24 54 76 90 120 124 180 190 246 250 280 294 316 346 370	420177340934