Prime p₀= 2134594546386726077 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 52 2 76 2 76 2 52 2 (?)
a_n: 0 2 54 56 132 134 210 212 264 266
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: Landjunge
db: batch=80, k=10, 2 52 2 76 2

SPT(16)	2134592568876918191	0 38 56 66 90 96 98 122 126 150 152 158 182 192 210 248	-1977509807886
STPT(10)	2134592627782907597	0 2 30 32 42 44 54 56 84 86	-1918603818480
SPT(16)	2134593293351992871	0 12 68 72 90 110 126 158 180 212 228 248 266 270 326 338	-1253034733206
STPT(10)	2134593581006766359	0 2 18 20 30 32 42 44 60 62	-965379959718
TPT(14)	2134594165916296919	0 2 18 20 48 50 72 74 90 92 102 104 132 134	-380470429158
SPT(16)	2134594533743499871	0 16 36 60 66 70 72 88 120 136 138 142 148 172 192 208	-12643226206
SPT(16)	2134594562521831117	0 22 24 52 60 82 130 142 234 246 294 316 324 352 354 376	16135105040
STPT(10)	2134594597089495377	0 2 42 44 72 74 102 104 144 146	50702769300
SPT(16)	2134595196071216713	0 6 16 30 126 136 168 246 268 346 378 388 484 498 508 514	649684490636
SPT(16)	2134595314403651107	0 4 16 42 52 72 82 144 262 324 334 354 364 390 402 406	768016925030
TPT(14)	2134595750587571441	0 2 78 80 126 128 186 188 216 218 228 230 240 242	1204200845364