Prime p₀= 690581396546574851 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 46 2 16 2 112 2 34 2 28 2 (?)
a_n: 0 2 48 50 66 68 180 182 216 218 246 248
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: 248
Found by: Theadalus
db: batch=72, k=12, 46 16 112 34 28

TPT(12)	690581251245348467	0 2 30 32 42 44 90 92 102 104 240 242	-145301226384
SPT(16)	690581269455397721	0 56 102 126 128 146 150 192 416 458 462 480 482 506 552 608	-127091177130
SPT(16)	690581320274051279	0 2 42 132 168 188 198 240 332 374 384 404 440 530 570 572	-76272523572
TPT(12)	690581322332479217	0 2 12 14 90 92 162 164 204 206 252 254	-74214095634
TPT(12)	690581346583195097	0 2 30 32 42 44 60 62 114 116 162 164	-49963379754
TPT(12)	690581362218644249	0 2 12 14 90 92 132 134 138 140 150 152	-34327930602
SPT(16)	690581441786526973	0 30 40 78 100 124 144 160 294 310 330 354 376 414 424 454	45239952122
TPT(12)	690581533812660671	0 2 18 20 60 62 150 152 198 200 240 242	137266085820
TPT(12)	690581534894423111	0 2 30 32 120 122 156 158 186 188 288 290	138347848260
SPT(16)	690581538287330477	0 30 72 182 216 260 266 270 296 300 306 350 384 494 536 566	141740755626
TPT(12)	690581543650634729	0 2 18 20 30 32 42 44 90 92 168 170	147104059878