Prime p₀= 10577805178836167 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 22 2 4 2 10 2 16 2 22 2 (?)
a_n: 0 2 24 26 30 32 42 44 60 62 84 86
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: 86
Found by: crashtech
db: batch=62, k=12, 22 4 10 16 22

SPT(14)	10577764548445799	0 8 14 38 50 74 78 104 108 132 144 168 174 182	-40630390368
SPT(14)	10577784778121551	0 70 72 90 112 148 160 168 180 216 238 256 258 328	-20400714616
SPT(14)	10577785690597987	0 16 36 60 64 66 114 136 184 186 190 214 234 250	-19488238180
SPT(14)	10577786020836721	0 16 22 40 46 66 100 108 142 162 168 186 192 208	-19157999446
SPT(14)	10577790122852059	0 42 48 60 78 90 100 120 130 142 160 172 178 220	-15055984108
SPT(14)	10577797320821603	0 14 38 66 80 104 108 116 120 144 158 186 210 224	-7858014564
SPT(16)	10577813228441831	0 36 42 50 66 78 80 92 126 138 140 152 168 176 182 218	8049605664
SPT(16)	10577817340830227	0 12 36 120 152 200 206 210 242 246 252 300 332 416 440 452	12161994060
STPT(10)	10577818685675819	0 2 48 50 90 92 132 134 180 182	13506839652
SPT(14)	10577834531240321	0 50 92 102 116 126 132 170 176 186 200 210 252 302	29352404154
SPT(14)	10577844283990769	0 30 32 74 104 108 128 144 164 168 198 240 242 272	39105154602