Prime p₀= 782394067380332987 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: [SG-2W]Kurzer
db: batch=73, k=12, 2 22 2 4 2 22

SPT(16)	782391863246317531	0 102 232 256 268 286 336 340 408 412 462 480 492 516 646 748	-2204134015456
TPT(14)	782391995960427947	0 2 42 44 162 164 210 212 264 266 330 332 360 362	-2071419905040
SPT(16)	782392557478068221	0 12 20 26 60 72 86 90 152 156 170 182 216 222 230 242	-1509902264766
STPT(10)	782392563955320551	0 2 36 38 78 80 120 122 156 158	-1503425012436
SPT(16)	782393534971691767	0 4 34 36 60 66 70 112 144 186 190 196 220 222 252 256	-532408641220
STPT(10)	782393907149821409	0 2 42 44 60 62 78 80 120 122	-160230511578
SPT(16)	782394270881563811	0 18 56 80 116 150 186 216 242 272 308 342 378 402 440 458	203501230824
STPT(10)	782394329811554531	0 2 36 38 78 80 120 122 156 158	262431221544
TPT(14)	782394335659233809	0 2 12 14 30 32 72 74 120 122 150 152 180 182	268278900822
STPT(10)	782394579088400849	0 2 18 20 30 32 42 44 60 62	511708067862
STPT(12)	782395031837916269	0 2 12 14 42 44 48 50 78 80 90 92	964457583282