Prime p₀= 2559887748168256547 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 28 2 22 2 4 2 22 2 28 2 (?)
a_n: 0 2 30 32 54 56 60 62 84 86 114 116
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: 116
Found by: JayPi
db: batch=82, k=12, 2 28 2 22 2 4

SPT(16)	2559886830929570543	0 18 24 36 56 78 114 128 246 260 296 318 338 350 356 374	-917238686004
SPT(16)	2559886843035289709	0 8 50 60 78 84 110 128 144 162 188 194 212 222 264 272	-905132966838
SPT(16)	2559886934988621773	0 30 38 56 104 126 168 174 230 236 278 300 348 366 374 404	-813179634774
SPT(16)	2559887069969797559	0 18 38 60 84 122 138 192 260 314 330 368 392 414 434 452	-678198458988
STPT(10)	2559887070716222549	0 2 42 44 120 122 198 200 240 242	-677452033998
SPT(16)	2559887271886511207	0 36 54 56 60 116 144 156 200 212 240 296 300 302 320 356	-476281745340
SPT(16)	2559887752113263227	0 24 40 52 60 66 90 96 160 166 190 196 204 216 232 256	3945006680
SPT(16)	2559888060110965891	0 6 30 58 150 178 192 238 240 286 300 328 420 448 472 478	311942709344
SPT(16)	2559888574753988581	0 12 28 70 78 90 108 160 180 232 250 262 270 312 328 340	826585732034
STPT(10)	2559888603454555181	0 2 6 8 48 50 90 92 96 98	855286298634
SPT(16)	2559888717916403473	0 18 28 34 108 130 136 144 160 168 174 196 270 276 286 304	969748146926