Prime p₀= 4374667802842985231 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 76 2 28 2 28 2 76 2 (?)
a_n: 0 2 78 80 108 110 138 140 216 218
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: 218
Found by: [SG]KidDoesCrunch
db: batch=85, k=10, 2 76 2 28 2

SPT(16)	4374666773001561511	0 18 48 82 118 126 138 142 156 160 172 180 216 250 280 298	-1029841423720
SPT(16)	4374667145080150883	0 18 56 110 150 156 170 198 266 294 308 314 354 408 446 464	-657762834348
STPT(10)	4374667258370598359	0 2 18 20 30 32 42 44 60 62	-544472386872
STPT(10)	4374667282554641921	0 2 30 32 60 62 90 92 120 122	-520288343310
STPT(10)	4374667472690783501	0 2 30 32 78 80 126 128 156 158	-330152201730
SPT(16)	4374667732720065611	0 18 36 56 80 90 122 140 168 186 218 228 252 272 290 308	-70122919620
TPT(14)	4374668034954177341	0 2 6 8 78 80 108 110 138 140 210 212 216 218	232111192110
STPT(14)	4374668034954177341	0 2 6 8 78 80 108 110 138 140 210 212 216 218	232111192110
SPT(16)	4374668535727014887	0 32 62 92 120 134 174 186 260 272 312 326 354 384 414 446	732884029656
SPT(16)	4374668607226550851	0 30 58 108 186 192 220 280 378 438 466 472 550 600 628 658	804383565620
SPT(16)	4374668651795343703	0 18 28 40 54 180 208 214 240 246 274 400 414 426 436 454	848952358472