Prime p₀= 1247268731341060397 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 58 2 58 2 10 2 (?)
a_n: 0 2 12 14 72 74 132 134 144 146
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: 146
Found by: Cruncher Pete
db: batch=77, k=10, 2 10 2 58 2

SPT(16)	1247267857950368203	0 10 24 60 66 78 88 136 138 186 196 208 214 250 264 274	-873390692194
STPT(10)	1247268109048167917	0 2 42 44 72 74 102 104 144 146	-622292892480
SPT(16)	1247268258784872293	0 60 68 78 84 116 120 144 170 194 198 230 236 246 254 314	-472556188104
TPT(14)	1247268411035910761	0 2 36 38 180 182 246 248 276 278 390 392 408 410	-320305149636
TPT(14)	1247268426918423737	0 2 120 122 300 302 330 332 450 452 480 482 504 506	-304422636660
SPT(16)	1247268680228573153	0 6 30 50 60 78 86 90 224 228 236 254 264 284 308 314	-51112487244
SPT(16)	1247268960902065219	0 24 48 60 70 84 88 154 174 240 244 258 268 280 304 328	229561004822
SPT(16)	1247268968561287613	0 18 50 74 134 156 186 198 266 278 308 330 390 414 446 464	237220227216
SPT(16)	1247269074015458723	0 8 54 78 138 144 150 180 188 218 224 230 290 314 360 368	342674398326
STPT(10)	1247269326449012561	0 2 30 32 60 62 90 92 120 122	595107952164
STPT(10)	1247269500038465999	0 2 18 20 30 32 42 44 60 62	768697405602