Prime p₀= 293815423574992721 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 76 2 28 2 28 2 76 2 58 2 (?)
a_n: 0 2 78 80 108 110 138 140 216 218 276 278
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: 278
Found by: [AF>EDLS] GGTF
db: batch=69, k=12, 76 28 28 76 58

SPT(14)	293815279027084327	0 16 24 52 84 102 112 144 154 172 204 232 240 256	-144547908394
SPT(14)	293815282128117401	0 18 56 72 80 108 158 210 260 288 296 312 350 368	-141446875320
SPT(14)	293815347809521579	0 48 54 70 108 112 132 220 240 244 282 298 304 352	-75765471142
SPT(14)	293815359975273593	0 8 56 66 78 90 108 146 164 176 188 198 246 254	-63599719128
SPT(14)	293815372124240873	0 14 54 60 74 78 90 98 110 114 128 134 174 188	-51450751848
TPT(12)	293815375258934741	0 2 36 38 78 80 186 188 198 200 216 218	-48316057980
STPT(10)	293815423574992721	0 2 78 80 108 110 138 140 216 218	0
SPT(14)	293815435058831009	0 2 18 32 78 80 122 168 210 212 258 272 288 290	11483838288
SPT(14)	293815439438810309	0 14 54 62 74 80 104 108 132 138 150 158 198 212	15863817588
SPT(14)	293815450632356929	0 12 22 28 48 82 108 124 150 184 204 210 220 232	27057364208
SPT(14)	293815453249327109	0 18 42 44 114 140 144 158 162 188 258 260 284 302	29674334388