Prime p₀= 2268501057606916997 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 40 2 28 2 28 2 40 2 (?)
a_n: 0 2 42 44 72 74 102 104 144 146
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: 146
Found by: Orange Kid
db: batch=81, k=10, 2 40 2 28 2

SPT(16)	2268500433012266837	0 20 102 174 182 194 212 222 242 252 270 282 290 362 444 464	-624594650160
SPT(16)	2268500437233960569	0 2 8 30 38 68 90 120 182 212 234 264 272 294 300 302	-620372956428
SPT(16)	2268500495245728979	0 4 42 60 70 88 130 132 250 252 294 312 322 340 378 382	-562361188018
STPT(10)	2268500649902359217	0 2 72 74 102 104 132 134 204 206	-407704557780
STPT(10)	2268500747104408247	0 2 12 14 72 74 132 134 144 146	-310502508750
SPT(16)	2268501028501237759	0 22 42 48 64 84 120 130 192 202 238 258 274 280 300 322	-29105679238
SPT(16)	2268501109460309257	0 6 46 52 114 150 226 262 294 330 406 442 504 510 550 556	51853392260
SPT(16)	2268501320314990769	0 2 42 50 54 98 114 158 204 248 264 308 312 320 360 362	262708073772
TPT(14)	2268501461622138131	0 2 138 140 156 158 240 242 306 308 336 338 366 368	404015221134
SPT(16)	2268501534582830441	0 6 26 38 48 90 108 116 222 230 248 290 300 312 332 338	476975913444
SPT(16)	2268501556698354683	0 26 44 110 114 144 156 210 224 278 290 320 324 390 408 434	499091437686