Prime p₀= 1233812382015608567 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 28 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 72 74 84 86
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: 86
Found by: MarkRBright
db: batch=77, k=10, 2 10 2 28 2

SPT(16)	1233811036817811323	0 6 26 84 126 134 144 156 158 170 180 188 230 288 308 314	-1345197797244
SPT(16)	1233811214593333231	0 60 88 102 118 142 190 192 196 198 246 270 286 300 328 388	-1167422275336
STPT(10)	1233811438200173969	0 2 42 44 90 92 138 140 180 182	-943815434598
STPT(10)	1233811610047135739	0 2 42 44 90 92 138 140 180 182	-771968472828
SPT(16)	1233811708423371083	0 24 86 96 116 164 186 240 320 374 396 444 464 474 536 560	-673592237484
STPT(10)	1233812239723463549	0 2 30 32 120 122 210 212 240 242	-142292145018
SPT(16)	1233812394084338461	0 12 28 66 78 130 136 138 220 222 228 280 292 330 346 358	12068729894
STPT(10)	1233812590599526919	0 2 42 44 60 62 78 80 120 122	208583918352
STPT(10)	1233812768640594809	0 2 78 80 120 122 162 164 240 242	386624986242
SPT(16)	1233812802619204681	0 18 48 60 70 100 142 156 172 186 228 258 268 280 310 328	420603596114
STPT(10)	1233812948445754217	0 2 30 32 72 74 114 116 144 146	566430145650