Prime p₀= 2310397508975629259 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 16 2 10 2 10 2 16 2 (?)
a_n: 0 2 18 20 30 32 42 44 60 62
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: 62
Found by: FritzB
db: batch=81, k=10, 2 16 2 10 2

SPT(16)	2310396536557689599	0 8 12 32 50 60 120 122 180 182 242 252 270 290 294 302	-972417939660
STPT(10)	2310396664393020701	0 2 36 38 78 80 120 122 156 158	-844582608558
STPT(10)	2310396813092786321	0 2 36 38 78 80 120 122 156 158	-695882842938
STPT(10)	2310397348847097407	0 2 60 62 72 74 84 86 144 146	-160128531852
SPT(16)	2310397418488435459	0 52 94 102 112 120 148 178 204 234 262 270 280 288 330 382	-90487193800
SPT(16)	2310397484816849803	0 6 16 34 58 64 114 148 216 250 300 306 330 348 358 364	-24158779456
STPT(10)	2310397570343435117	0 2 30 32 42 44 54 56 84 86	61367805858
SPT(16)	2310397665709725733	0 36 40 64 96 114 124 138 166 180 190 208 240 264 268 304	156734096474
TPT(14)	2310397762084045631	0 2 6 8 48 50 60 62 156 158 180 182 186 188	253108416372
TPT(14)	2310397903807184309	0 2 30 32 60 62 150 152 180 182 318 320 378 380	394831555050
SPT(16)	2310397912247624471	0 20 26 30 32 48 60 68 90 98 110 126 128 132 138 158	403271995212