Prime p₀= 3717715452896465651 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 34 2 40 2 40 2 34 2 (?)
a_n: 0 2 36 38 78 80 120 122 156 158
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: 158
Found by: Sphynx
db: batch=84, k=10, 2 34 2 40 2

SPT(16)	3717714474153522211	0 6 10 36 42 108 150 160 168 178 220 286 292 318 322 328	-978742943440
SPT(18)	3717714551518591817	0 20 42 62 110 116 140 200 222 224 246 306 330 336 384 404 426 446	-901377873834
SPT(16)	3717714590273992519	0 28 60 82 144 168 204 228 274 298 334 358 420 442 474 502	-862622473132
SPT(16)	3717715078780023323	0 6 56 78 116 158 168 186 290 308 318 360 398 420 470 476	-374116442328
STPT(10)	3717715210475767547	0 2 54 56 72 74 90 92 144 146	-242420698104
STPT(10)	3717715407597489209	0 2 18 20 30 32 42 44 60 62	-45298976442
STPT(10)	3717715936276209389	0 2 18 20 30 32 42 44 60 62	483379743738
SPT(16)	3717715968822480349	0 30 40 114 118 138 148 252 280 384 394 414 418 492 502 532	515926014698
STPT(10)	3717716019909257489	0 2 12 14 30 32 48 50 60 62	567012791838
SPT(13)	3717716206188829969	0 12 60 90 192 210 222 234 252 354 384 432 444	753292364318
STPT(10)	3717716930859852629	0 2 42 44 60 62 78 80 120 122	1477963386978