Prime p₀= 2136775625694653759 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 16 2 16 2 10 2 (?)
a_n: 0 2 12 14 30 32 48 50 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: TheKillerChicken
db: batch=80, k=10, 2 10 2 16 2

SPT(16)	2136774484387116139	0 24 30 70 114 130 132 142 210 220 222 238 282 322 328 352	-1141307537620
TPT(14)	2136774619263849197	0 2 12 14 24 26 90 92 150 152 174 176 252 254	-1006430804562
SPT(16)	2136775286768158447	0 6 12 34 52 60 66 112 144 190 196 204 222 244 250 256	-338926495312
SPT(16)	2136775316378522357	0 26 66 146 186 194 264 290 336 362 432 440 480 560 600 626	-309316131402
SPT(16)	2136775409835211973	0 66 78 80 84 120 168 230 234 296 344 380 384 386 398 464	-215859441786
TPT(14)	2136775569247319597	0 2 42 44 84 86 102 104 120 122 132 134 240 242	-56447334162
SPT(16)	2136775637363889553	0 6 10 58 84 96 126 166 168 208 238 250 276 324 328 334	11669235794
STPT(10)	2136775640393162957	0 2 24 26 42 44 60 62 84 86	14698509198
SPT(16)	2136775756295410151	0 8 18 20 36 38 48 50 108 110 120 122 138 140 150 158	130600756392
STPT(12)	2136775756295410169	0 2 18 20 30 32 90 92 102 104 120 122	130600756410
TPT(14)	2136775882464221891	0 2 60 62 90 92 138 140 156 158 168 170 270 272	256769568132