Prime p₀= 1556689572686396969 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: crashtech
db: batch=78, k=10, 2 40 2 16 2

SPT(16)	1556688761820950509	0 22 42 70 82 100 114 120 202 208 222 240 252 280 300 322	-810865446460
SPT(16)	1556689113855104497	0 52 72 76 100 136 160 162 184 186 210 246 270 274 294 346	-458831292472
SPT(13)	1556689498172930021	0 42 102 120 150 180 186 192 222 252 270 330 372	-74513466948
STPT(10)	1556689508783598587	0 2 30 32 72 74 114 116 144 146	-63902798382
SPT(18)	1556689516723698529	0 28 58 82 90 130 132 154 160 222 228 250 252 292 300 324 354 382	-55962698440
STPT(10)	1556689536167060717	0 2 90 92 102 104 114 116 204 206	-36519336252
SPT(16)	1556689775415450821	0 26 48 66 80 90 96 182 186 272 278 288 302 320 342 368	202729053852
STPT(10)	1556689834772725517	0 2 12 14 72 74 132 134 144 146	262086328548
SPT(16)	1556689985316532513	0 16 18 24 28 58 66 84 100 118 126 156 160 166 168 184	412630135544
STPT(10)	1556690062577914079	0 2 12 14 90 92 168 170 180 182	489891517110
SPT(16)	1556690111718664073	0 20 48 74 78 116 128 156 158 186 198 236 240 266 294 314	539032267104