Prime p₀= 2539745651754140537 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 10 2 4 2 10 2 10 2 (?)
a_n: 0 2 12 14 24 26 30 32 42 44 54 56
All 12 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 56
Found by: JayPi
db: batch=82, k=12, 2 10 2 10 2 4

SPT(16)	2539743241189998647	0 42 44 72 90 182 206 212 234 240 264 356 374 402 404 446	-2410564141890
SPT(16)	2539743259878830483	0 14 60 98 104 134 144 170 174 200 210 240 246 284 330 344	-2391875310054
SPT(16)	2539743284679675691	0 66 78 106 138 148 168 192 196 220 240 250 282 310 322 388	-2367074464846
SPT(20)	2539743825908545381	0 10 82 88 132 160 168 192 196 210 388 402 406 430 438 466 510 516 588 598	-1825845595156
STPT(10)	2539744988405283479	0 2 18 20 30 32 42 44 60 62	-663348857058
STPT(10)	2539745256412534031	0 2 36 38 78 80 120 122 156 158	-395341606506
TPT(14)	2539746037470294377	0 2 30 32 174 176 240 242 270 272 282 284 294 296	385716153840
SPT(16)	2539746182718509629	0 34 54 88 102 124 138 172 210 244 258 280 294 328 348 382	530964369092
SPT(16)	2539746420421470241	0 36 46 60 108 120 130 142 156 168 178 190 238 252 262 298	768667329704
STPT(10)	2539746456889472429	0 2 18 20 30 32 42 44 60 62	805135331892
SPT(16)	2539746515374424311	0 18 46 102 112 130 148 190 228 270 288 306 316 372 400 418	863620283774