Prime p₀= 2582239695574870757 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 22 2 4 2 22 2 4 2 22 2 (?)
a_n: 0 2 24 26 30 32 54 56 60 62 84 86
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: 86
Found by: JayPi
db: batch=82, k=12, 2 22 2 4 2 22

STPT(10)	2582237530935603377	0 2 12 14 72 74 132 134 144 146	-2164639267380
STPT(10)	2582237562424320917	0 2 30 32 42 44 54 56 84 86	-2133150549840
SPT(16)	2582238089399097083	0 6 38 86 96 126 146 170 216 240 260 290 300 348 380 386	-1606175773674
SPT(16)	2582238138000316879	0 18 48 168 184 240 262 282 340 360 382 438 454 574 604 622	-1557574553878
SPT(16)	2582238495255884449	0 24 34 40 48 52 150 174 208 232 330 334 342 348 358 382	-1200318986308
STPT(10)	2582238612887393111	0 2 36 38 78 80 120 122 156 158	-1082687477646
SPT(16)	2582240267923940647	0 22 24 30 34 46 90 150 196 256 300 312 316 322 324 346	572349069890
SPT(16)	2582240949319448701	0 6 30 76 96 142 180 196 216 232 270 316 336 382 406 412	1253744577944
SPT(16)	2582241454721335111	0 12 28 96 112 118 126 160 168 202 210 216 232 300 316 328	1759146464354
STPT(10)	2582242305780682841	0 2 6 8 18 20 30 32 36 38	2610205812084
SPT(16)	2582242342215859373	0 8 14 30 36 144 228 240 254 266 350 458 464 480 486 494	2646640988616