Prime p₀= 4387510515662887757 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: [SG]KidDoesCrunch
db: batch=85, k=10, 2 40 2 28 2

SPT(16)	4387506724870977677	0 6 162 180 204 254 266 270 296 300 312 362 386 404 560 566	-3790791910080
STPT(10)	4387508038089069077	0 2 30 32 60 62 90 92 120 122	-2477573818680
SPT(16)	4387508070418468783	0 16 28 90 154 184 190 204 250 264 270 300 364 426 438 454	-2445244418974
STPT(10)	4387509577207924511	0 2 36 38 78 80 120 122 156 158	-938454963246
SPT(16)	4387509771591967913	0 36 78 84 120 126 138 156 158 176 188 194 230 236 278 314	-744070919844
SPT(16)	4387510204078454207	0 20 44 60 66 86 126 174 266 314 354 374 380 396 420 440	-311584433550
SPT(16)	4387510721664511633	0 30 64 96 100 118 126 156 208 238 246 264 268 300 334 364	206001623876
SPT(16)	4387511306503292927	0 14 36 42 56 102 116 126 170 180 194 240 254 260 282 296	790840405170
STPT(10)	4387511843130956591	0 2 6 8 18 20 30 32 36 38	1327468068834
SPT(16)	4387512093557362709	0 2 8 80 84 90 104 170 252 318 332 338 342 414 420 422	1577894474952
TPT(14)	4387512332052728171	0 2 18 20 60 62 138 140 210 212 228 230 276 278	1816389840414