Prime p₀= 2256730056016690979 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 16 2 10 2 28 2 10 2 16 2 (?)
a_n: 0 2 18 20 30 32 60 62 72 74 90 92
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: 92
Found by: Orange Kid
db: batch=81, k=12, 2 16 2 10 2 28

SPT(16)	2256728554282297111	0 48 76 78 106 148 150 168 220 238 240 282 310 312 340 388	-1501734393868
STPT(10)	2256728602207903259	0 2 18 20 60 62 102 104 120 122	-1453808787720
SPT(16)	2256728675701797953	0 50 60 68 78 104 116 138 266 288 300 326 336 344 354 404	-1380314893026
SPT(16)	2256729632135674769	0 42 54 72 90 108 110 150 152 192 194 212 230 248 260 302	-423881016210
TPT(14)	2256729763218032981	0 2 60 62 216 218 270 272 306 308 336 338 420 422	-292798657998
SPT(13)	2256730006745712791	0 12 72 138 192 258 300 342 408 462 528 588 600	-49270978188
SPT(16)	2256730186946767243	0 10 18 40 54 60 66 76 138 148 154 160 174 196 204 214	130930076264
STPT(10)	2256730515223015859	0 2 18 20 30 32 42 44 60 62	459206324880
SPT(16)	2256730837475828249	0 8 48 50 72 90 120 128 144 152 182 200 222 224 264 272	781459137270
STPT(10)	2256731198746216637	0 2 30 32 42 44 54 56 84 86	1142729525658
STPT(10)	2256731458046993867	0 2 30 32 60 62 90 92 120 122	1402030302888