Prime p₀= 76167251203703279 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 70 2 64 2 28 2 28 2 22 2 (?)
a_n: 0 2 72 74 138 140 168 170 198 200 222 224
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: 224
Found by: emoga
db: batch=67, k=12, 70 64 28 28 22

TPT(14)	76167196192519979	0 2 72 74 162 164 198 200 222 224 240 242 252 254	-55011183300
TPT(12)	76167210027275459	0 2 72 74 78 80 120 122 138 140 180 182	-41176427820
STPT(10)	76167223037744981	0 2 6 8 18 20 30 32 36 38	-28165958298
SPT(14)	76167231613898791	0 6 22 66 70 78 88 90 100 108 112 156 172 178	-19589804488
TPT(12)	76167232668350849	0 2 60 62 102 104 240 242 252 254 312 314	-18535352430
SPT(14)	76167232902682069	0 12 24 58 70 102 142 180 220 252 264 298 310 322	-18301021210
SPT(14)	76167255825837151	0 16 82 96 120 162 178 180 196 238 262 276 342 358	4622133872
SPT(14)	76167261824402041	0 12 28 88 90 112 142 168 198 220 222 282 298 310	10620698762
TPT(12)	76167271132889309	0 2 18 20 42 44 60 62 90 92 102 104	19929186030
SPT(14)	76167272999498881	0 78 88 96 106 148 166 210 228 270 280 288 298 376	21795795602
SPT(14)	76167280871898163	0 30 78 136 190 204 208 276 280 294 348 406 454 484	29668194884