Prime p₀= 5322344703135011 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 124 2 10 2 130 2 64 2 28 2 (?)
a_n: 0 2 126 128 138 140 270 272 336 338 366 368
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: 368
Found by: Alez
db: batch=61, k=12, 124 10 130 64 28

SPT(14)	5322291086442193	0 34 40 48 58 64 76 78 90 96 106 114 120 154	-53616692818
SPT(16)	5322293038241423	0 26 38 54 66 74 110 114 140 144 180 188 200 216 228 254	-51664893588
TPT(12)	5322296124863747	0 2 42 44 54 56 150 152 162 164 210 212	-48578271264
SPT(14)	5322318166460381	0 32 56 60 140 162 176 192 206 228 308 312 336 368	-26536674630
TPT(12)	5322326179765211	0 2 36 38 78 80 138 140 210 212 240 242	-18523369800
SPT(14)	5322328095979423	0 6 16 34 46 84 90 100 106 144 156 174 184 190	-16607155588
SPT(14)	5322347612621651	0 8 122 126 170 182 218 240 276 288 332 336 450 458	2909486640
SPT(14)	5322357053606561	0 42 62 68 80 96 132 146 182 198 210 216 236 278	12350471550
SPT(14)	5322365604917797	0 42 52 90 94 100 130 156 186 192 196 234 244 286	20901782786
SPT(14)	5322369412738163	0 8 24 38 60 78 80 144 146 164 186 200 216 224	24709603152
SPT(14)	5322370001244463	0 18 30 40 58 60 84 154 178 180 198 208 220 238	25298109452