Prime p₀= 264550705325006129 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 10 2 58 2 4 2 28 2 52 2 (?)
a_n: 0 2 12 14 72 74 78 80 108 110 162 164
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: 164
Found by: Megacruncher
db: batch=69, k=12, 10 58 4 28 52

SPT(14)	264550606824318469	0 30 58 142 210 222 240 310 328 340 408 492 520 550	-98500687660
SPT(14)	264550634559128509	0 4 18 30 48 72 100 102 130 154 172 184 198 202	-70765877620
SPT(16)	264550654057235773	0 6 24 28 30 36 64 76 108 120 148 154 156 160 178 184	-51267770356
SPT(14)	264550655000765411	0 26 32 38 50 66 98 120 152 168 180 186 192 218	-50324240718
SPT(14)	264550661573465851	0 12 52 58 78 82 90 100 108 112 132 138 178 190	-43751540278
SPT(14)	264550685593326991	0 46 70 88 130 138 162 256 280 288 330 348 372 418	-19731679138
TPT(12)	264550710654662891	0 2 96 98 138 140 180 182 186 188 258 260	5329656762
STPT(10)	264550719716675471	0 2 30 32 78 80 126 128 156 158	14391669342
SPT(14)	264550746964105271	0 18 80 90 98 102 108 140 146 150 158 168 230 248	41639099142
SPT(14)	264550748548459937	0 6 56 90 102 132 156 200 224 254 266 300 350 356	43223453808
TPT(12)	264550772109821291	0 2 6 8 48 50 66 68 78 80 90 92	66784815162