Prime p₀= 3565055598930446441 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 4 2 10 2 10 2 4 2 (?)
a_n: 0 2 6 8 18 20 30 32 36 38
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: 38
Found by: [SG]KidDoesCrunch
db: batch=84, k=10, 2 4 2 10 2

SPT(16)	3565055239232204659	0 12 22 148 208 214 258 298 414 454 498 504 564 690 700 712	-359698241782
SPT(16)	3565055248729978963	0 24 36 94 100 124 150 154 276 280 306 330 336 394 406 430	-350200467478
STPT(10)	3565055262475228517	0 2 30 32 72 74 114 116 144 146	-336455217924
TPT(14)	3565055335616071307	0 2 84 86 90 92 162 164 174 176 264 266 330 332	-263314375134
SPT(16)	3565055344795778677	0 4 42 54 72 114 120 132 154 166 172 214 232 244 282 286	-254134667764
STPT(10)	3565055474418057869	0 2 18 20 30 32 42 44 60 62	-124512388572
STPT(12)	3565055745749048651	0 2 48 50 78 80 168 170 198 200 246 248	146818602210
STPT(10)	3565055862190128377	0 2 30 32 42 44 54 56 84 86	263259681936
STPT(10)	3565056069092918117	0 2 42 44 132 134 222 224 264 266	470162471676
STPT(10)	3565056162296414081	0 2 6 8 18 20 30 32 36 38	563365967640
SPT(16)	3565056232381945957	0 12 60 66 82 94 96 112 144 160 162 174 190 196 244 256	633451499516