Prime p₀= 4374667258370598359 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 16 2 10 2 10 2 16 2 (?)
a_n: 0 2 18 20 30 32 42 44 60 62
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: 62
Found by: [SG]KidDoesCrunch
db: batch=85, k=10, 2 16 2 10 2

STPT(10)	4374665240389458059	0 2 12 14 90 92 168 170 180 182	-2017981140300
SPT(16)	4374666004703138231	0 66 68 98 126 140 146 152 246 252 258 272 300 330 332 398	-1253667460128
STPT(10)	4374666036689917229	0 2 18 20 30 32 42 44 60 62	-1221680681130
SPT(16)	4374666538454528917	0 46 54 72 82 96 144 174 262 292 340 354 364 382 390 436	-719916069442
SPT(16)	4374666773001561511	0 18 48 82 118 126 138 142 156 160 172 180 216 250 280 298	-485369036848
SPT(16)	4374667145080150883	0 18 56 110 150 156 170 198 266 294 308 314 354 408 446 464	-113290447476
STPT(10)	4374667282554641921	0 2 30 32 60 62 90 92 120 122	24184043562
STPT(10)	4374667472690783501	0 2 30 32 78 80 126 128 156 158	214320185142
SPT(16)	4374667732720065611	0 18 36 56 80 90 122 140 168 186 218 228 252 272 290 308	474349467252
STPT(10)	4374667802842985231	0 2 78 80 108 110 138 140 216 218	544472386872
TPT(14)	4374668034954177341	0 2 6 8 78 80 108 110 138 140 210 212 216 218	776583578982