Prime p₀= 2309967221264258627 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 28 2 10 2 10 2 28 2 (?)
a_n: 0 2 30 32 42 44 54 56 84 86
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: 86
Found by: FritzB
db: batch=81, k=10, 2 28 2 10 2

SPT(16)	2309965957966791353	0 84 116 138 150 186 204 228 326 350 368 404 416 438 470 554	-1263297467274
SPT(16)	2309966260834666463	0 68 80 98 120 150 156 176 228 248 254 284 306 324 336 404	-960429592164
SPT(16)	2309966709190805671	0 6 10 90 108 130 168 220 336 388 426 448 466 546 550 556	-512073452956
STPT(10)	2309966850552120437	0 2 30 32 42 44 54 56 84 86	-370712138190
STPT(10)	2309966938582438307	0 2 42 44 72 74 102 104 144 146	-282681820320
STPT(10)	2309967153645666839	0 2 18 20 30 32 42 44 60 62	-67618591788
SPT(16)	2309967376114789211	0 18 20 30 32 72 80 108 140 168 176 216 218 228 230 248	154850530584
SPT(16)	2309967674776637297	0 24 50 90 122 200 206 312 314 420 426 504 536 576 602 626	453512378670
STPT(10)	2309967726411101717	0 2 42 44 102 104 162 164 204 206	505146843090
SPT(16)	2309967826235053211	0 2 30 62 68 108 122 128 132 138 152 192 198 230 258 260	604970794584
SPT(18)	2309967948423260669	0 38 42 98 120 144 152 162 188 264 290 300 308 332 354 410 414 452	727159002042