Prime p₀= 799800159481797569 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: crashtech
db: batch=73, k=10, 2 16 2 10 2

SPT(16)	799797927309030487	0 6 10 40 70 84 154 180 190 216 286 300 330 360 364 370	-2232172767082
SPT(18)	799798073359382893	0 34 48 144 190 214 256 274 286 288 300 318 360 384 430 526 540 574	-2086122414676
STPT(10)	799798674232023647	0 2 30 32 42 44 54 56 84 86	-1485249773922
SPT(16)	799798816990380503	0 14 18 50 66 108 126 128 156 158 176 218 234 266 270 284	-1342491417066
SPT(16)	799798900020561829	0 12 34 40 112 138 222 292 330 400 484 510 582 588 610 622	-1259461235740
STPT(10)	799799284008586619	0 2 18 20 30 32 42 44 60 62	-875473210950
SPT(16)	799800323902819543	0 28 36 94 126 178 210 220 264 274 306 358 390 448 456 484	164421021974
SPT(16)	799800414803292697	0 42 60 70 90 112 120 142 144 166 174 196 216 226 244 286	255321495128
SPT(16)	799800599808773671	0 12 16 40 52 82 120 162 196 238 276 306 318 342 346 358	440326976102
STPT(10)	799800614440551569	0 2 18 20 30 32 42 44 60 62	454958754000
SPT(16)	799800670038556741	0 46 48 66 70 90 148 156 190 198 256 276 280 298 300 346	510556759172