Prime p₀= 356681344009374779 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 40 2 4 2 40 2 16 2 58 2 (?)
a_n: 0 2 42 44 48 50 90 92 108 110 168 170
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: 170
Found by: [SG-2W]Kurzer
db: batch=70, k=12, 40 4 40 16 58

STPT(10)	356681286501128777	0 2 24 26 42 44 60 62 84 86	-57508246002
SPT(16)	356681288967455693	0 8 86 90 140 170 230 248 306 324 384 414 464 468 546 554	-55041919086
SPT(14)	356681294691452009	0 2 42 138 180 182 188 234 240 242 284 380 420 422	-49317922770
SPT(14)	356681318751835163	0 36 38 86 108 120 140 144 164 176 198 246 248 284	-25257539616
SPT(14)	356681324352096209	0 30 32 42 50 60 78 152 170 180 188 198 200 230	-19657278570
SPT(14)	356681331212913607	0 40 42 66 96 130 180 262 312 346 376 400 402 442	-12796461172
TPT(12)	356681362743891707	0 2 30 32 90 92 240 242 354 356 420 422	18734516928
SPT(14)	356681375249592577	0 46 60 66 126 160 186 220 246 280 340 346 360 406	31240217798
SPT(14)	356681421478075847	0 2 44 96 104 116 132 164 180 192 200 252 294 296	77468701068
SPT(14)	356681437914018979	0 10 24 40 42 100 142 180 222 280 282 298 312 322	93904644200
SPT(14)	356681439534909199	0 28 90 118 142 162 184 228 250 270 294 322 384 412	95525534420