Prime p₀= 1681298874751683137 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 28 2 10 2 10 2 28 2 (?)
a_n: 0 2 30 32 42 44 54 56 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: amazing
db: batch=79, k=10, 2 28 2 10 2

TPT(14)	1681297098398595569	0 2 48 50 78 80 90 92 138 140 150 152 258 260	-1776353087568
SPT(16)	1681297216693472269	0 12 42 52 180 190 192 198 232 238 240 250 378 388 418 430	-1658058210868
SPT(16)	1681297317262439273	0 14 74 80 90 116 140 180 194 234 258 284 294 300 360 374	-1557489243864
SPT(16)	1681297827729005951	0 12 48 62 86 108 126 128 150 152 170 192 216 230 266 278	-1047022677186
SPT(20)	1681298358399008309	0 38 44 74 114 134 158 192 212 252 290 330 350 384 408 428 468 498 504 542	-516352674828
SPT(16)	1681298850976415519	0 14 24 50 78 134 140 144 224 228 234 290 318 344 354 368	-23775267618
SPT(16)	1681299088959186563	0 74 110 126 188 224 276 284 300 308 360 396 458 474 510 584	214207503426
SPT(16)	1681299401148452587	0 22 64 90 102 120 150 160 204 214 244 262 274 300 342 364	526396769450
SPT(16)	1681299703051025327	0 26 30 32 44 84 92 186 320 414 422 462 474 476 480 506	828299342190
STPT(12)	1681299714995356877	0 2 24 26 42 44 192 194 210 212 234 236	840243673740
STPT(10)	1681299743977690049	0 2 12 14 90 92 168 170 180 182	869226006912