Prime p₀= 2068565922329692571 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: Cruncher Pete
db: batch=80, k=10, 2 34 2 40 2

STPT(10)	2068564729064001401	0 2 30 32 78 80 126 128 156 158	-1193265691170
STPT(10)	2068564773127458797	0 2 90 92 102 104 114 116 204 206	-1149202233774
STPT(10)	2068564853107250549	0 2 42 44 60 62 78 80 120 122	-1069222442022
STPT(10)	2068565472422805371	0 2 36 38 78 80 120 122 156 158	-449906887200
SPT(16)	2068565574206903539	0 10 22 28 48 78 84 94 108 118 124 154 174 180 192 202	-348122789032
SPT(16)	2068565911876922149	0 42 54 82 84 118 150 202 300 352 384 418 420 448 460 502	-10452770422
STPT(10)	2068566569024475209	0 2 18 20 30 32 42 44 60 62	646694782638
STPT(10)	2068567234578190469	0 2 12 14 30 32 48 50 60 62	1312248497898
SPT(16)	2068567496089380067	0 6 22 40 60 112 136 162 220 246 270 322 342 360 376 382	1573759687496
TPT(14)	2068567571883695147	0 2 12 14 72 74 114 116 144 146 150 152 192 194	1649554002576
STPT(12)	2068567780379069579	0 2 42 44 78 80 162 164 198 200 240 242	1858049377008