Prime p₀= 1337258527646639501 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 76 2 40 2 4 2 40 2 76 2 (?)
a_n: 0 2 78 80 120 122 126 128 168 170 246 248
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: 248
Found by: Dirk Broer
db: batch=77, k=12, 2 76 2 40 2 4

SPT(16)	1337256269810862571	0 22 36 102 108 130 136 178 210 252 258 280 286 352 366 388	-2257835776930
SPT(16)	1337256571960421759	0 44 104 128 138 180 194 230 258 294 308 350 360 384 444 488	-1955686217742
SPT(16)	1337256953305362211	0 12 28 36 40 66 136 160 168 192 262 288 292 300 316 328	-1574341277290
SPT(16)	1337257418003814677	0 54 56 66 86 102 156 192 314 350 404 420 440 450 452 506	-1109642824824
STPT(10)	1337258112843531407	0 2 42 44 72 74 102 104 144 146	-414803108094
TPT(14)	1337258162231530241	0 2 6 8 48 50 126 128 180 182 300 302 336 338	-365415109260
STPT(12)	1337258681557328069	0 2 12 14 72 74 78 80 138 140 150 152	153910688568
STPT(10)	1337259110643698687	0 2 30 32 42 44 54 56 84 86	582997059186
TPT(14)	1337259179819514641	0 2 6 8 126 128 180 182 228 230 240 242 258 260	652172875140
STPT(10)	1337259336447020057	0 2 30 32 42 44 54 56 84 86	808800380556
STPT(10)	1337259428502674177	0 2 54 56 72 74 90 92 144 146	900856034676