Prime p₀= 2727134114937421067 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 2 4 30 26 10 48 6 14 6 48 10 26 30 4 2 (?)
a_n: 0 2 6 36 62 72 120 126 140 146 194 204 230 260 264 266
All 16 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 266
Found by: Ben
db: batch=82, k=16, 2 4 30 26 10 48 6 14

SPT(16)	2727132636675624647	0 60 86 92 140 144 182 210 236 264 302 306 354 360 386 446	-1478261796420
TPT(14)	2727132803989924241	0 2 18 20 60 62 156 158 168 170 270 272 288 290	-1310947496826
STPT(10)	2727132927860340029	0 2 18 20 30 32 42 44 60 62	-1187077081038
STPT(10)	2727133153620166097	0 2 42 44 72 74 102 104 144 146	-961317254970
SPT(16)	2727133301978923391	0 38 42 66 80 86 116 138 170 192 222 228 242 266 270 308	-812958497676
SPT(16)	2727133325532140443	0 10 18 76 106 178 204 228 286 310 336 408 438 496 504 514	-789405280624
STPT(10)	2727134390292281087	0 2 24 26 42 44 60 62 84 86	275354860020
SPT(16)	2727134859968426581	0 6 16 42 90 112 172 196 216 240 300 322 370 396 406 412	745031005514
SPT(16)	2727135533718337493	0 20 24 44 96 170 174 180 224 230 234 308 360 380 384 404	1418780916426
SPT(16)	2727135783670794173	0 44 60 84 138 146 188 200 264 276 318 326 380 404 420 464	1668733373106
TPT(14)	2727136071216735287	0 2 102 104 174 176 180 182 282 284 390 392 420 422	1956279314220