Prime p₀= 1231519810147867307 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: Megacruncher
db: batch=77, k=10, 2 10 2 28 2

SPT(16)	1231519149827771821	0 22 60 78 136 156 186 190 198 202 232 252 310 328 366 388	-660320095486
SPT(18)	1231519454907741211	0 66 142 150 172 196 202 226 268 270 312 336 342 366 388 396 472 538	-355240126096
STPT(10)	1231519621581085349	0 2 42 44 60 62 78 80 120 122	-188566781958
SPT(16)	1231519766333622593	0 14 20 84 86 128 144 156 188 200 216 258 260 324 330 344	-43814244714
STPT(10)	1231519788076102529	0 2 12 14 90 92 168 170 180 182	-22071764778
TPT(14)	1231519809243503651	0 2 48 50 126 128 180 182 210 212 240 242 300 302	-904363656
SPT(16)	1231519946408437729	0 60 120 124 154 162 208 234 268 294 340 348 378 382 442 502	136260570422
SPT(16)	1231520070473656207	0 24 40 84 96 114 144 154 282 292 322 340 352 396 412 436	260325788900
STPT(10)	1231520172010830431	0 2 36 38 78 80 120 122 156 158	361862963124
STPT(12)	1231520509528166267	0 2 12 14 54 56 60 62 102 104 114 116	699380298960
SPT(16)	1231520656822914961	0 18 40 46 48 72 90 96 172 178 196 220 222 228 250 268	846675047654