Prime p₀= 1251909696148959431 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 34 2 40 2 58 2 40 2 34 2 (?)
a_n: 0 2 36 38 78 80 138 140 180 182 216 218
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: 218
Found by: Cruncher Pete
db: batch=77, k=12, 2 34 2 40 2 58

STPT(10)	1251909567141878327	0 2 12 14 72 74 132 134 144 146	-129007081104
SPT(16)	1251909581718456289	0 18 24 30 54 90 114 132 150 168 192 228 252 258 264 282	-114430503142
STPT(10)	1251909600914818007	0 2 30 32 42 44 54 56 84 86	-95234141424
TPT(14)	1251909655098041627	0 2 72 74 162 164 240 242 294 296 312 314 330 332	-41050917804
STPT(10)	1251909679398452741	0 2 6 8 18 20 30 32 36 38	-16750506690
SPT(16)	1251909695136726091	0 12 22 70 72 88 100 120 148 168 180 196 198 246 256 268	-1012233340
SPT(16)	1251909865367952409	0 24 82 160 178 180 244 300 322 378 442 444 462 540 598 622	169218992978
STPT(10)	1251909979646052437	0 2 60 62 72 74 84 86 144 146	283497093006
STPT(10)	1251910449267446831	0 2 36 38 78 80 120 122 156 158	753118487400
STPT(10)	1251910870203062891	0 2 6 8 48 50 90 92 96 98	1174054103460
SPT(16)	1251911051419923061	0 16 40 48 58 72 90 96 112 118 136 150 160 168 192 208	1355270963630