Prime p₀= 1247269500038465999 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 16 2 10 2 10 2 16 2 (?)
a_n: 0 2 18 20 30 32 42 44 60 62
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: 62
Found by: Cruncher Pete
db: batch=77, k=10, 2 16 2 10 2

SPT(16)	1247268680228573153	0 6 30 50 60 78 86 90 224 228 236 254 264 284 308 314	-819809892846
STPT(10)	1247268731341060397	0 2 12 14 72 74 132 134 144 146	-768697405602
SPT(16)	1247268960902065219	0 24 48 60 70 84 88 154 174 240 244 258 268 280 304 328	-539136400780
SPT(16)	1247268968561287613	0 18 50 74 134 156 186 198 266 278 308 330 390 414 446 464	-531477178386
SPT(16)	1247269074015458723	0 8 54 78 138 144 150 180 188 218 224 230 290 314 360 368	-426023007276
STPT(10)	1247269326449012561	0 2 30 32 60 62 90 92 120 122	-173589453438
STPT(10)	1247269959505610861	0 2 6 8 18 20 30 32 36 38	459467144862
STPT(10)	1247270229005199689	0 2 12 14 90 92 168 170 180 182	728966733690
SPT(20)	1247270244604290079	0 28 84 94 172 192 262 274 328 370 372 414 468 480 550 570 648 658 714 742	744565824080
STPT(10)	1247270253239475761	0 2 6 8 18 20 30 32 36 38	753201009762
STPT(10)	1247270413237441259	0 2 18 20 30 32 42 44 60 62	913198975260