Prime p₀= 1231520953019494589 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 76 2 76 2 10 2 (?)
a_n: 0 2 12 14 90 92 168 170 180 182
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: 182
Found by: Megacruncher
db: batch=77, k=10, 2 10 2 76 2

SPT(16)	1231520070473656207	0 24 40 84 96 114 144 154 282 292 322 340 352 396 412 436	-882545838382
STPT(10)	1231520172010830431	0 2 36 38 78 80 120 122 156 158	-781008664158
STPT(12)	1231520509528166267	0 2 12 14 54 56 60 62 102 104 114 116	-443491328322
SPT(16)	1231520656822914961	0 18 40 46 48 72 90 96 172 178 196 220 222 228 250 268	-296196579628
STPT(10)	1231520913035908667	0 2 12 14 72 74 132 134 144 146	-39983585922
STPT(10)	1231520916446480741	0 2 6 8 48 50 90 92 96 98	-36573013848
SPT(16)	1231520969076538961	0 38 56 62 86 120 150 228 230 308 338 372 396 402 420 458	16057044372
STPT(10)	1231521023770852817	0 2 30 32 60 62 90 92 120 122	70751358228
TPT(14)	1231521125089109537	0 2 90 92 174 176 210 212 270 272 312 314 354 356	172069614948
STPT(10)	1231521172944573521	0 2 6 8 48 50 90 92 96 98	219925078932
TPT(14)	1231521177517521167	0 2 90 92 102 104 114 116 132 134 144 146 180 182	224498026578