Prime p₀= 2577451622795290907 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 28 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 72 74 84 86
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: 86
Found by: Roadranner
db: batch=82, k=10, 2 10 2 28 2

SPT(16)	2577450920611092023	0 38 80 84 98 108 110 168 176 234 236 246 260 264 306 344	-702184198884
TPT(14)	2577451024375726097	0 2 54 56 240 242 282 284 300 302 354 356 432 434	-598419564810
SPT(16)	2577451109873302043	0 14 20 44 50 120 140 150 188 198 218 288 294 318 324 338	-512921988864
TPT(14)	2577451357261212281	0 2 36 38 48 50 78 80 90 92 120 122 150 152	-265534078626
STPT(10)	2577451391349450521	0 2 6 8 48 50 90 92 96 98	-231445840386
SPT(16)	2577451552160206853	0 6 36 74 96 146 180 204 206 230 264 314 336 374 404 410	-70635084054
SPT(16)	2577451861430504749	0 4 28 34 48 94 108 130 168 190 204 250 264 270 294 298	238635213842
STPT(10)	2577451939586463851	0 2 6 8 18 20 30 32 36 38	316791172944
SPT(16)	2577452018891266007	0 66 86 110 116 134 144 150 170 176 186 204 210 234 254 320	396095975100
SPT(16)	2577452198198345851	0 28 52 66 106 108 118 130 168 180 190 192 232 246 270 298	575403054944
STPT(12)	2577452243227907921	0 2 30 32 78 80 120 122 168 170 198 200	620432617014