Prime p₀= 4365136262371067789 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 76 2 76 2 10 2 (?)
a_n: 0 2 12 14 90 92 168 170 180 182
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: 182
Found by: [SG]ATA-Rolf
db: batch=85, k=10, 2 10 2 76 2

SPT(16)	4365135352716484981	0 10 60 120 162 186 220 270 298 348 382 406 448 508 558 568	-909654582808
STPT(10)	4365135552513142499	0 2 78 80 120 122 162 164 240 242	-709857925290
SPT(16)	4365135608512412711	0 38 42 50 60 80 108 162 206 260 288 308 318 326 330 368	-653858655078
SPT(16)	4365135658770704569	0 22 58 70 78 90 100 148 174 222 232 244 252 264 300 322	-603600363220
SPT(16)	4365135906385822753	0 30 96 124 126 136 154 160 174 180 198 208 210 238 304 334	-355985245036
STPT(12)	4365136052108060039	0 2 30 32 72 74 108 110 150 152 180 182	-210263007750
SPT(16)	4365136304636196637	0 60 70 100 126 132 160 172 174 186 214 220 246 276 286 346	42265128848
SPT(16)	4365136434615929279	0 20 42 48 62 72 164 192 230 258 350 360 374 380 402 422	172244861490
SPT(16)	4365136604167415771	0 32 90 92 132 156 158 182 246 270 272 296 336 338 396 428	341796347982
SPT(18)	4365136768706293631	0 32 42 56 90 98 102 120 146 162 188 206 210 218 252 266 276 308	506335225842
STPT(12)	4365137032371474299	0 2 12 14 42 44 48 50 78 80 90 92	770000406510