Prime p₀= 810222250211556617 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 10 2 4 2 10 2 10 2 (?)
a_n: 0 2 12 14 24 26 30 32 42 44 54 56
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: 56
Found by: [AF>Amis des Lapins] Ceclo
db: batch=73, k=12, 2 10 2 10 2 4

SPT(16)	810221413356257011	0 6 22 40 72 132 142 222 310 390 400 460 492 510 526 532	-836855299606
STPT(10)	810221626705919117	0 2 30 32 42 44 54 56 84 86	-623505637500
STPT(10)	810221776159091897	0 2 30 32 42 44 54 56 84 86	-474052464720
SPT(16)	810221864017520813	0 14 50 78 80 96 110 140 174 204 218 234 236 264 300 314	-386194035804
STPT(12)	810221965982539127	0 2 12 14 42 44 90 92 120 122 132 134	-284229017490
SPT(16)	810222122440408511	0 8 18 30 56 86 98 116 210 228 240 270 296 308 318 326	-127771148106
STPT(10)	810222290140618637	0 2 42 44 72 74 102 104 144 146	39929062020
SPT(16)	810222397243715671	0 36 70 88 90 102 130 138 160 168 196 208 210 228 262 298	147032159054
STPT(10)	810222498738048467	0 2 30 32 120 122 210 212 240 242	248526491850
STPT(10)	810222881789097911	0 2 36 38 78 80 120 122 156 158	631577541294
STPT(10)	810223132805814071	0 2 36 38 78 80 120 122 156 158	882594257454