Prime p₀= 2068538041265436371 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 118 2 16 2 16 2 118 2 (?)
a_n: 0 2 120 122 138 140 156 158 276 278
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: 278
Found by: Cruncher Pete
db: batch=80, k=10, 2 118 2 16 2

SPT(16)	2068536261617600081	0 26 60 66 72 110 128 150 158 180 198 236 242 248 282 308	-1779647836290
SPT(16)	2068536466805772949	0 10 34 112 124 144 172 214 300 342 370 390 402 480 504 514	-1574459663422
SPT(16)	2068536701971457203	0 54 58 84 114 126 150 154 180 184 208 220 250 276 280 334	-1339293979168
STPT(10)	2068537213758321737	0 2 54 56 72 74 90 92 144 146	-827507114634
STPT(10)	2068537264455813581	0 2 78 80 108 110 138 140 216 218	-776809622790
STPT(10)	2068537546506672557	0 2 30 32 42 44 54 56 84 86	-494758763814
STPT(10)	2068538698503012641	0 2 6 8 48 50 90 92 96 98	657237576270
STPT(10)	2068538771436958781	0 2 36 38 78 80 120 122 156 158	730171522410
SPT(16)	2068538903431253329	0 42 52 88 108 112 130 142 168 180 198 202 222 258 268 310	862165816958
STPT(10)	2068538981272054607	0 2 30 32 42 44 54 56 84 86	940006618236
SPT(16)	2068539107895035021	0 8 12 26 50 86 96 110 168 182 192 228 252 266 270 278	1066629598650