Prime p₀= 238702222159992467 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 112 2 16 2 28 2 106 2 40 2 (?)
a_n: 0 2 114 116 132 134 162 164 270 272 312 314
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: 314
Found by: Megacruncher
db: batch=69, k=12, 112 16 28 106 40

SPT(14)	238702168152566401	0 40 78 90 132 136 142 216 222 226 268 280 318 358	-54007426066
SPT(14)	238702169744407147	0 6 30 34 94 102 126 160 184 192 252 256 280 286	-52415585320
SPT(14)	238702197968291963	0 78 80 96 104 140 146 168 174 210 218 234 236 314	-24191700504
SPT(14)	238702205730766651	0 40 52 60 66 126 132 136 142 202 208 216 228 268	-16429225816
SPT(16)	238702207538567209	0 12 30 42 90 94 162 220 222 280 348 352 400 412 430 442	-14621425258
TPT(12)	238702209867930047	0 2 30 32 54 56 72 74 192 194 282 284	-12292062420
TPT(12)	238702228258178129	0 2 12 14 18 20 90 92 168 170 222 224	6098185662
SPT(14)	238702235838240403	0 36 40 60 78 88 94 180 186 196 214 234 238 274	13678247936
SPT(14)	238702239599905181	0 6 8 50 90 116 122 126 132 158 198 240 242 248	17439912714
SPT(14)	238702252512260507	0 42 80 104 144 150 152 174 176 182 222 246 284 326	30352268040
TPT(12)	238702255978454969	0 2 72 74 108 110 138 140 150 152 180 182	33818462502