Prime p₀= 729350133554102237 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 58 2 10 2 10 2 58 2 (?)
a_n: 0 2 60 62 72 74 84 86 144 146
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: MarkRBright
db: batch=73, k=10, 2 58 2 10 2

SPT(16)	729348632293560107	0 2 24 56 86 92 114 132 164 182 204 210 240 272 294 296	-1501260542130
STPT(10)	729349146590084087	0 2 12 14 42 44 72 74 84 86	-986964018150
SPT(16)	729349429464215083	0 6 94 130 166 174 216 250 264 298 340 348 384 420 508 514	-704089887154
STPT(10)	729349604133022421	0 2 6 8 48 50 90 92 96 98	-529421079816
STPT(10)	729349777296548459	0 2 18 20 60 62 102 104 120 122	-356257553778
SPT(16)	729349847764931047	0 6 40 42 54 130 132 180 196 244 246 322 334 336 370 376	-285789171190
SPT(16)	729350492199137399	0 30 42 50 78 108 122 170 330 378 392 422 450 458 470 500	358645035162
SPT(16)	729351208603581593	0 38 50 56 60 68 78 86 108 116 126 134 138 144 156 194	1075049479356
STPT(10)	729351297989770271	0 2 6 8 48 50 90 92 96 98	1164435668034
TPT(14)	729351862151790191	0 2 150 152 186 188 198 200 270 272 276 278 306 308	1728597687954
SPT(16)	729352630770228613	0 16 54 64 126 144 150 196 264 310 316 334 396 406 444 460	2497216126376