Prime p₀= 2071129321029682997 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 28 2 40 2 40 2 28 2 (?)
a_n: 0 2 30 32 72 74 114 116 144 146
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 28 2 40 2

SPT(16)	2071127123734342987	0 22 60 102 126 132 162 180 286 304 334 340 364 406 444 466	-2197295340010
STPT(10)	2071127359588051937	0 2 42 44 72 74 102 104 144 146	-1961441631060
STPT(10)	2071128815936424059	0 2 12 14 30 32 48 50 60 62	-505093258938
SPT(16)	2071128848240594833	0 18 34 36 66 94 130 168 196 234 270 298 328 330 346 364	-472789088164
STPT(10)	2071128982833603347	0 2 54 56 72 74 90 92 144 146	-338196079650
SPT(16)	2071129027587391613	0 20 50 90 140 144 204 210 344 350 410 414 464 504 534 554	-293442291384
TPT(14)	2071129468706642219	0 2 12 14 30 32 42 44 72 74 78 80 108 110	147676959222
SPT(16)	2071129567549145837	0 24 56 110 122 170 174 180 266 272 276 324 336 390 422 446	246519462840
SPT(16)	2071130265303233873	0 14 110 120 156 168 204 296 348 440 476 488 524 534 630 644	944273550876
SPT(16)	2071130449016244289	0 34 78 88 120 150 154 190 198 234 238 268 300 310 354 388	1127986561292
STPT(10)	2071130583512776691	0 2 6 8 48 50 90 92 96 98	1262483093694