Prime p₀= 2310034513343147777 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 88 2 40 2 40 2 88 2 (?)
a_n: 0 2 90 92 132 134 174 176 264 266
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: 266
Found by: Orange Kid
db: batch=81, k=10, 2 88 2 40 2

SPT(16)	2310034007263676381	0 2 8 30 42 72 78 98 240 260 266 296 308 330 336 338	-506079471396
STPT(10)	2310034045359203027	0 2 42 44 72 74 102 104 144 146	-467983944750
SPT(16)	2310034055412517979	0 12 42 44 48 54 74 110 132 168 188 194 198 200 230 242	-457930629798
SPT(16)	2310034162331890957	0 22 36 42 70 84 114 132 154 172 202 216 244 250 264 286	-351011256820
SPT(16)	2310034342626493753	0 36 54 64 96 130 138 184 210 256 264 298 330 340 358 394	-170716654024
SPT(16)	2310034455882261469	0 18 30 40 60 72 132 154 258 280 340 352 372 382 394 412	-57460886308
SPT(16)	2310034824523441909	0 4 24 34 70 88 90 154 168 232 234 252 288 298 318 322	311180294132
SPT(16)	2310035674474342487	0 2 50 116 122 156 164 200 246 282 290 324 330 396 444 446	1161131194710
STPT(10)	2310035939711868131	0 2 30 32 78 80 126 128 156 158	1426368720354
STPT(10)	2310036259130292527	0 2 30 32 102 104 174 176 204 206	1745787144750
STPT(10)	2310036308361618041	0 2 6 8 18 20 30 32 36 38	1795018470264