Prime p₀= 2859918333046706471 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 64 2 58 2 22 2 58 2 64 2 (?)
a_n: 0 2 66 68 126 128 150 152 210 212 276 278
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: 278
Found by: Landjunge
db: batch=82, k=12, 2 64 2 58 2 22

SPT(16)	2859917595297182557	0 40 112 124 130 144 174 246 250 322 352 366 372 384 456 496	-737749523914
STPT(10)	2859917705727474617	0 2 30 32 42 44 54 56 84 86	-627319231854
TPT(14)	2859917785410977327	0 2 12 14 180 182 192 194 252 254 372 374 504 506	-547635729144
SPT(16)	2859917954140279423	0 28 34 66 70 150 156 160 174 178 184 264 268 300 306 334	-378906427048
SPT(16)	2859918265844099087	0 12 24 50 84 92 134 146 210 222 264 272 306 332 344 356	-67202607384
SPT(16)	2859918299039444341	0 10 12 66 70 96 102 112 210 220 226 252 256 310 312 322	-34007262130
SPT(16)	2859918423649655507	0 6 14 74 102 144 156 222 314 380 392 434 462 522 530 536	90602949036
SPT(16)	2859918926371861747	0 24 64 72 84 94 142 150 154 162 210 220 232 240 280 304	593325155276
TPT(14)	2859919248466822691	0 2 90 92 120 122 156 158 186 188 210 212 240 242	915420116220
TPT(14)	2859919474339867187	0 2 54 56 120 122 132 134 294 296 330 332 372 374	1141293160716
STPT(10)	2859919891491969737	0 2 12 14 72 74 132 134 144 146	1558445263266