Prime p₀= 2309613564267128417 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 82 2 46 2 46 2 82 2 (?)
a_n: 0 2 84 86 132 134 180 182 264 266
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: 266
Found by: FritzB
db: batch=81, k=10, 2 82 2 46 2

SPT(16)	2309612344900116679	0 12 22 54 78 112 114 142 180 208 210 244 268 300 310 322	-1219367011738
STPT(12)	2309612496031384877	0 2 12 14 54 56 90 92 132 134 144 146	-1068235743540
SPT(16)	2309612955906483187	0 30 36 64 72 94 102 114 142 154 162 184 192 220 226 256	-608360645230
STPT(10)	2309612983273730801	0 2 6 8 18 20 30 32 36 38	-580993397616
TPT(14)	2309613141514153157	0 2 12 14 102 104 114 116 132 134 174 176 210 212	-422752975260
SPT(16)	2309613536129512699	0 42 58 102 108 132 172 198 232 258 298 322 328 372 388 430	-28137615718
SPT(16)	2309613792902659609	0 10 18 64 70 94 112 130 132 150 168 192 198 244 252 262	228635531192
STPT(10)	2309613961246025219	0 2 42 44 120 122 198 200 240 242	396978896802
TPT(14)	2309613987874829969	0 2 12 14 48 50 210 212 240 242 378 380 480 482	423607701552
STPT(10)	2309614992459439079	0 2 18 20 30 32 42 44 60 62	1428192310662
SPT(16)	2309615279889074789	0 2 32 38 108 140 144 218 234 308 312 344 414 420 450 452	1715621946372