Prime p₀= 2778120437901756977 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 28 2 76 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 120 122 150 152 162 164
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: 164
Found by: JayPi
db: batch=82, k=12, 2 10 2 28 2 76

SPT(16)	2778117827651084309	0 20 42 80 84 98 108 132 230 254 264 278 282 320 342 362	-2610250672668
STPT(10)	2778118052557270637	0 2 30 32 42 44 54 56 84 86	-2385344486340
STPT(10)	2778118341891236711	0 2 6 8 48 50 90 92 96 98	-2096010520266
SPT(16)	2778119438639576309	0 24 42 78 98 108 122 150 152 180 194 204 224 260 278 302	-999262180668
STPT(10)	2778119554782925229	0 2 30 32 60 62 90 92 120 122	-883118831748
STPT(10)	2778119579410393199	0 2 42 44 60 62 78 80 120 122	-858491363778
SPT(13)	2778120537560563411	0 12 42 90 150 192 216 240 282 342 390 420 432	99658806434
STPT(10)	2778120711348472547	0 2 180 182 222 224 264 266 444 446	273446715570
STPT(10)	2778121118219091941	0 2 6 8 18 20 30 32 36 38	680317334964
SPT(16)	2778121222120580521	0 16 28 82 108 148 150 162 196 208 210 250 276 330 342 358	784218823544
SPT(16)	2778121301568709009	0 40 58 60 88 90 118 130 198 210 238 240 268 270 288 328	863666952032