Prime p₀= 1124727365410573019 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: crashtech
db: batch=76, k=10, 2 16 2 10 2

SPT(16)	1124724853106723269	0 18 84 100 168 172 178 232 240 294 300 304 372 388 454 472	-2512303849750
SPT(16)	1124725687283715931	0 10 22 36 58 78 82 96 112 126 130 150 172 186 198 208	-1678126857088
SPT(16)	1124725831202335249	0 10 42 82 130 138 144 154 198 208 214 222 270 310 342 352	-1534208237770
SPT(16)	1124726041469992187	0 2 30 134 144 186 204 240 296 332 350 392 402 506 534 536	-1323940580832
STPT(10)	1124726317355479409	0 2 18 20 30 32 42 44 60 62	-1048055093610
STPT(12)	1124727310473842939	0 2 12 14 42 44 78 80 108 110 120 122	-54936730080
SPT(16)	1124727557240654599	0 12 60 78 102 112 168 220 240 292 348 358 382 400 448 460	191830081580
SPT(16)	1124727880264381343	0 26 56 66 74 80 90 96 194 200 210 216 224 234 264 290	514853808324
SPT(16)	1124728099098742559	0 50 68 78 80 84 92 110 222 240 248 252 254 264 282 332	733688169540
TPT(14)	1124728412113066217	0 2 72 74 84 86 114 116 162 164 252 254 312 314	1046702493198
STPT(10)	1124728981089963881	0 2 30 32 78 80 126 128 156 158	1615679390862