Prime p₀= 64005256187354189 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 106 2 10 2 16 2 28 2 40 2 (?)
a_n: 0 2 108 110 120 122 138 140 168 170 210 212
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: 212
Found by: Vit Kliber
db: batch=67, k=12, 106 10 16 28 40

TPT(12)	64005213942387041	0 2 18 20 60 62 78 80 126 128 156 158	-42244967148
SPT(14)	64005217584551731	0 36 42 76 108 112 120 178 186 190 222 256 262 298	-38602802458
SPT(14)	64005225303632257	0 30 36 46 54 60 64 186 190 196 204 214 220 250	-30883721932
TPT(12)	64005239312133521	0 2 6 8 48 50 96 98 210 212 216 218	-16875220668
SPT(14)	64005240990295021	0 46 60 96 106 112 120 148 156 162 172 208 222 268	-15197059168
SPT(14)	64005252017518739	0 2 14 102 114 132 140 162 170 188 200 288 300 302	-4169835450
TPT(12)	64005264539683007	0 2 30 32 60 62 90 92 132 134 312 314	8352328818
SPT(14)	64005269019767599	0 42 72 94 130 144 174 220 250 264 300 322 352 394	12832413410
SPT(14)	64005273672381497	0 30 44 56 66 110 122 144 156 200 210 222 236 266	17485027308
SPT(14)	64005279848894353	0 34 84 100 126 168 180 244 256 298 324 340 390 424	23661540164
SPT(14)	64005284825559491	0 96 108 122 152 186 200 228 242 276 306 320 332 428	28638205302