Prime p₀= 1231515883693122257 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 22 2 16 2 16 2 22 2 (?)
a_n: 0 2 24 26 42 44 60 62 84 86
All 10 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 86
Found by: Megacruncher
db: batch=77, k=10, 2 22 2 16 2

SPT(16)	1231514461884439267	0 40 54 64 72 94 124 132 184 192 222 244 252 262 276 316	-1421808682990
SPT(16)	1231515063397094323	0 70 136 168 198 234 238 256 288 306 310 346 376 408 474 544	-820296027934
SPT(16)	1231515210021681239	0 18 32 50 54 90 92 120 152 180 182 218 222 240 254 272	-673671441018
SPT(16)	1231515265219809457	0 6 24 30 42 46 76 90 136 150 180 184 196 202 220 226	-618473312800
SPT(16)	1231515588841749061	0 12 60 82 112 156 160 162 250 252 256 300 330 352 400 412	-294851373196
STPT(10)	1231515651969958679	0 2 18 20 30 32 42 44 60 62	-231723163578
STPT(10)	1231516073055824909	0 2 108 110 150 152 192 194 300 302	189362702652
STPT(10)	1231516305805704179	0 2 18 20 30 32 42 44 60 62	422112581922
TPT(14)	1231516373862093017	0 2 12 14 24 26 54 56 72 74 114 116 180 182	490168970760
SPT(16)	1231516470117901829	0 12 14 44 54 68 98 102 110 114 144 158 168 198 200 212	586424779572
TPT(14)	1231516705158471887	0 2 72 74 114 116 150 152 234 236 264 266 282 284	821465349630