Prime p₀= 2068564853107250549 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)	2068564442065046087	0 2 30 32 42 44 54 56 84 86	-411042204462
SPT(16)	2068564467211124587	0 6 24 130 174 214 256 300 316 360 402 442 486 592 610 616	-385896125962
SPT(16)	2068564533106865141	0 6 78 90 152 162 206 210 398 402 446 456 518 530 602 608	-320000385408
SPT(16)	2068564630520707349	0 30 60 84 90 114 174 254 258 338 398 422 428 452 482 512	-222586543200
STPT(10)	2068564729064001401	0 2 30 32 78 80 126 128 156 158	-124043249148
STPT(10)	2068564773127458797	0 2 90 92 102 104 114 116 204 206	-79979791752
STPT(10)	2068565472422805371	0 2 36 38 78 80 120 122 156 158	619315554822
SPT(16)	2068565574206903539	0 10 22 28 48 78 84 94 108 118 124 154 174 180 192 202	721099652990
SPT(16)	2068565911876922149	0 42 54 82 84 118 150 202 300 352 384 418 420 448 460 502	1058769671600
STPT(10)	2068565922329692571	0 2 36 38 78 80 120 122 156 158	1069222442022
STPT(10)	2068566569024475209	0 2 18 20 30 32 42 44 60 62	1715917224660