Prime p₀= 70784049485987867 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 82 2 34 2 28 2 88 2 10 2 (?)
a_n: 0 2 84 86 120 122 150 152 240 242 252 254
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: 254
Found by: emoga
db: batch=67, k=12, 82 34 28 88 10

SPT(14)	70784021733214913	0 14 48 54 56 84 134 180 230 258 260 266 300 314	-27752772954
SPT(16)	70784023236894511	0 12 22 42 48 70 112 148 150 186 228 250 256 276 286 298	-26249093356
SPT(14)	70784024429432423	0 6 30 36 68 84 128 186 230 246 278 284 308 314	-25056555444
SPT(14)	70784029736832977	0 6 26 36 56 92 110 126 144 180 200 210 230 236	-19749154890
SPT(14)	70784034745159987	0 52 54 60 66 76 102 124 150 160 166 172 174 226	-14740827880
SPT(16)	70784041525942453	0 18 30 90 100 168 190 238 246 294 316 384 394 454 466 484	-7960045414
TPT(12)	70784061698285519	0 2 42 44 48 50 78 80 132 134 150 152	12212297652
STPT(10)	70784072739403997	0 2 30 32 42 44 54 56 84 86	23253416130
SPT(14)	70784083767266011	0 6 18 58 120 126 168 178 220 226 288 328 340 346	34281278144
SPT(16)	70784085179851129	0 28 94 108 120 130 150 154 234 238 258 268 280 294 360 388	35693863262
SPT(14)	70784090761618891	0 28 72 76 90 100 112 186 198 208 222 226 270 298	41275631024