Prime p₀= 2309951260677661397 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 22 2 16 2 16 2 22 2 (?)
a_n: 0 2 24 26 42 44 60 62 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: FritzB
db: batch=81, k=10, 2 22 2 16 2

SPT(16)	2309950437682562489	0 20 38 48 78 90 182 218 294 330 422 434 464 474 492 512	-822995098908
SPT(18)	2309950643459784839	0 8 24 92 98 152 198 210 222 290 302 314 360 414 420 488 504 512	-617217876558
SPT(16)	2309950805033362637	0 6 56 66 72 80 90 110 126 146 156 164 170 180 230 236	-455644298760
STPT(10)	2309951026103376779	0 2 12 14 90 92 168 170 180 182	-234574284618
SPT(16)	2309951093126747167	0 40 42 82 126 160 192 250 336 394 426 460 504 544 546 586	-167550914230
SPT(16)	2309951109992109799	0 42 54 64 78 88 102 172 270 340 354 364 378 388 400 442	-150685551598
SPT(18)	2309951364666585467	0 6 36 62 72 84 90 126 182 204 260 296 302 314 324 350 380 386	103988924070
SPT(16)	2309951531267010017	0 6 44 50 56 80 90 92 114 116 126 150 156 162 200 206	270589348620
STPT(10)	2309951906323392767	0 2 42 44 72 74 102 104 144 146	645645731370
STPT(10)	2309952310811006357	0 2 12 14 42 44 72 74 84 86	1050133344960
STPT(10)	2309952442121109827	0 2 30 32 42 44 54 56 84 86	1181443448430