Prime p₀= 1268523003633457499 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 16 2 40 2 16 2 10 2 (?)
a_n: 0 2 12 14 30 32 72 74 90 92 102 104
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: 104
Found by: Megacruncher
db: batch=77, k=12, 2 10 2 16 2 40

STPT(10)	1268522267272060811	0 2 6 8 48 50 90 92 96 98	-736361396688
TPT(14)	1268522267272060811	0 2 6 8 48 50 90 92 96 98 168 170 288 290	-736361396688
STPT(10)	1268522618176040387	0 2 30 32 42 44 54 56 84 86	-385457417112
SPT(16)	1268522914640322911	0 56 128 176 260 296 300 302 336 338 342 378 462 510 582 638	-88993134588
SPT(16)	1268522964165943903	0 18 70 114 120 124 130 138 190 198 204 208 214 258 310 328	-39467513596
TPT(14)	1268523003633457421	0 2 78 80 90 92 108 110 150 152 168 170 180 182	-78
SPT(16)	1268523022828192063	0 10 18 148 154 174 184 214 594 624 634 654 660 790 798 808	19194734564
SPT(16)	1268523044499204727	0 10 34 60 114 126 132 136 150 154 160 172 226 252 276 286	40865747228
STPT(10)	1268523106064564771	0 2 36 38 78 80 120 122 156 158	102431107272
TPT(14)	1268523132896652317	0 2 42 44 84 86 102 104 144 146 240 242 312 314	129263194818
STPT(10)	1268523608687334887	0 2 30 32 42 44 54 56 84 86	605053877388