Prime p₀= 2068537213758321737 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 52 2 16 2 16 2 52 2 (?)
a_n: 0 2 54 56 72 74 90 92 144 146
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: 146
Found by: Cruncher Pete
db: batch=80, k=10, 2 52 2 16 2

STPT(10)	2068535047323266057	0 2 30 32 42 44 54 56 84 86	-2166435055680
SPT(16)	2068535240666124409	0 40 112 130 142 160 168 204 208 244 252 270 282 300 372 412	-1973092197328
SPT(16)	2068535947960674421	0 12 28 40 78 88 106 132 166 192 210 220 258 270 286 298	-1265797647316
SPT(16)	2068536261617600081	0 26 60 66 72 110 128 150 158 180 198 236 242 248 282 308	-952140721656
SPT(16)	2068536466805772949	0 10 34 112 124 144 172 214 300 342 370 390 402 480 504 514	-746952548788
SPT(16)	2068536701971457203	0 54 58 84 114 126 150 154 180 184 208 220 250 276 280 334	-511786864534
STPT(10)	2068537264455813581	0 2 78 80 108 110 138 140 216 218	50697491844
STPT(10)	2068537546506672557	0 2 30 32 42 44 54 56 84 86	332748350820
STPT(10)	2068538041265436371	0 2 120 122 138 140 156 158 276 278	827507114634
STPT(10)	2068538698503012641	0 2 6 8 48 50 90 92 96 98	1484744690904
STPT(10)	2068538771436958781	0 2 36 38 78 80 120 122 156 158	1557678637044