Prime p₀= 2310514002339153431 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 4 2 10 2 10 2 4 2 (?)
a_n: 0 2 6 8 18 20 30 32 36 38
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: 38
Found by: FritzB
db: batch=81, k=10, 2 4 2 10 2

SPT(16)	2310512846398237321	0 36 58 70 88 120 136 148 150 162 178 210 228 240 262 298	-1155940916110
STPT(10)	2310513017443260281	0 2 36 38 78 80 120 122 156 158	-984895893150
TPT(14)	2310513030195848657	0 2 12 14 54 56 102 104 114 116 174 176 180 182	-972143304774
STPT(10)	2310513357056647109	0 2 48 50 90 92 132 134 180 182	-645282506322
SPT(16)	2310513727958697301	0 10 28 36 78 102 130 162 286 318 346 370 412 420 438 448	-274380456130
TPT(14)	2310513961052585837	0 2 24 26 84 86 300 302 360 362 414 416 444 446	-41286567594
SPT(16)	2310514120681672211	0 42 96 108 116 122 138 152 216 230 246 252 260 272 326 368	118342518780
SPT(16)	2310514235234757931	0 22 36 42 66 82 100 222 250 372 390 406 430 436 450 472	232895604500
SPT(16)	2310514312740629167	0 16 40 42 72 84 100 126 130 156 172 184 214 216 240 256	310401475736
STPT(10)	2310515013916363997	0 2 30 32 42 44 54 56 84 86	1011577210566
SPT(16)	2310515210546737541	0 42 78 92 116 146 176 198 230 252 282 312 336 350 386 428	1208207584110