Prime p₀= 2568502320730465727 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 52 2 28 2 64 2 28 2 52 2 (?)
a_n: 0 2 54 56 84 86 150 152 180 182 234 236
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: 236
Found by: Penguin
db: batch=82, k=12, 2 52 2 28 2 64

SPT(16)	2568501165896333959	0 12 42 100 102 118 142 184 198 240 264 280 282 340 370 382	-1154834131768
STPT(10)	2568501169911095687	0 2 30 32 72 74 114 116 144 146	-1150819370040
TPT(14)	2568501236088073367	0 2 90 92 144 146 222 224 252 254 264 266 312 314	-1084642392360
SPT(16)	2568501576308440007	0 2 6 30 32 42 44 72 104 132 134 144 146 170 174 176	-744422025720
SPT(16)	2568502094477963263	0 58 70 100 148 168 196 210 244 258 286 306 354 384 396 454	-226252502464
TPT(14)	2568502236155924987	0 2 72 74 90 92 144 146 174 176 312 314 372 374	-84574540740
STPT(10)	2568502385045432159	0 2 18 20 30 32 42 44 60 62	64314966432
STPT(10)	2568502424723519201	0 2 30 32 78 80 126 128 156 158	103993053474
STPT(10)	2568502511325564629	0 2 12 14 30 32 48 50 60 62	190595098902
SPT(16)	2568502734831632569	0 24 48 64 94 112 168 202 210 244 300 318 348 364 388 412	414101166842
STPT(10)	2568503328231795137	0 2 30 32 42 44 54 56 84 86	1007501329410