Prime p₀= 2309681055494379767 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 28 2 40 2 40 2 28 2 (?)
a_n: 0 2 30 32 72 74 114 116 144 146
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: FritzB
db: batch=81, k=10, 2 28 2 40 2

SPT(16)	2309679592145369879	0 18 80 128 152 164 242 282 290 330 408 420 444 492 554 572	-1463349009888
STPT(10)	2309679748370942069	0 2 48 50 90 92 132 134 180 182	-1307123437698
SPT(16)	2309679749433085933	0 28 124 168 198 204 238 298 390 450 484 490 520 564 660 688	-1306061293834
TPT(14)	2309680052204796911	0 2 48 50 96 98 120 122 210 212 318 320 378 380	-1003289582856
TPT(14)	2309680368869054969	0 2 12 14 72 74 102 104 132 134 240 242 282 284	-686625324798
STPT(10)	2309680386564454661	0 2 6 8 18 20 30 32 36 38	-668929925106
STPT(10)	2309681545680953441	0 2 6 8 48 50 90 92 96 98	490186573674
SPT(16)	2309681693152665701	0 6 18 20 38 116 156 216 242 302 342 420 438 440 452 458	637658285934
SPT(16)	2309681746281339511	0 12 46 48 72 102 130 138 160 168 196 226 250 252 286 298	690786959744
SPT(16)	2309681802059873981	0 20 90 126 180 218 230 258 308 336 348 386 440 476 546 566	746565494214
SPT(16)	2309682080114009771	0 18 36 42 62 126 150 158 360 368 392 456 476 482 500 518	1024619630004