Prime p₀= 1248278022550841057 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: Cruncher Pete
db: batch=77, k=10, 2 10 2 28 2

SPT(16)	1248277261879403351	0 12 36 56 72 78 92 128 150 186 200 206 222 242 266 278	-760671437706
STPT(10)	1248277595484605039	0 2 48 50 90 92 132 134 180 182	-427066236018
SPT(16)	1248277813298580061	0 12 46 60 70 112 130 166 186 222 240 282 292 306 340 352	-209252260996
STPT(10)	1248277825171477277	0 2 60 62 72 74 84 86 144 146	-197379363780
SPT(16)	1248277829396994923	0 18 114 128 140 150 170 174 200 204 224 234 246 260 356 374	-193153846134
SPT(16)	1248278006982106853	0 90 104 168 188 224 230 258 260 288 294 330 350 414 428 518	-15568734204
SPT(16)	1248278051136694493	0 6 14 18 26 44 48 90 194 236 240 258 266 270 278 284	28585853436
SPT(16)	1248278182655465959	0 22 34 48 78 88 130 138 154 162 204 214 244 258 270 292	160104624902
SPT(16)	1248278637402592801	0 40 76 82 90 96 120 132 196 208 232 238 246 252 288 328	614851751744
SPT(16)	1248279181101869209	0 10 28 42 88 90 108 160 192 244 262 264 310 324 342 352	1158551028152
TPT(14)	1248279286447391369	0 2 150 152 210 212 330 332 342 344 378 380 402 404	1263896550312