Prime p₀= 2068564016972401769 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 40 2 16 2 16 2 40 2 (?)
a_n: 0 2 42 44 60 62 78 80 120 122
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: 122
Found by: Cruncher Pete
db: batch=80, k=10, 2 40 2 16 2

STPT(10)	2068563280036472027	0 2 12 14 72 74 132 134 144 146	-736935929742
STPT(10)	2068563523042428857	0 2 30 32 42 44 54 56 84 86	-493929972912
STPT(10)	2068563663048532421	0 2 36 38 78 80 120 122 156 158	-353923869348
SPT(16)	2068563705274000289	0 20 42 54 62 84 98 104 138 144 158 180 188 200 222 242	-311698401480
STPT(10)	2068563781889540237	0 2 30 32 42 44 54 56 84 86	-235082861532
SPT(16)	2068563821998451773	0 4 10 64 66 114 118 238 276 396 400 448 450 504 510 514	-194973949996
SPT(16)	2068564314854598637	0 6 24 40 70 90 124 150 160 186 220 240 270 286 304 310	297882196868
STPT(10)	2068564442065046087	0 2 30 32 42 44 54 56 84 86	425092644318
SPT(16)	2068564467211124587	0 6 24 130 174 214 256 300 316 360 402 442 486 592 610 616	450238722818
SPT(16)	2068564533106865141	0 6 78 90 152 162 206 210 398 402 446 456 518 530 602 608	516134463372
SPT(16)	2068564630520707349	0 30 60 84 90 114 174 254 258 338 398 422 428 452 482 512	613548305580