Prime p₀= 2725701497935277357 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: Cruncher Pete
db: batch=82, k=10, 2 10 2 28 2

SPT(18)	2725700919224437279	0 12 58 60 82 88 112 114 142 180 208 210 234 240 262 264 310 322	-578710840078
SPT(16)	2725700925412677257	0 14 84 146 156 170 240 246 260 266 336 350 360 422 492 506	-572522600100
SPT(16)	2725701000933242161	0 22 40 60 142 162 168 222 316 370 376 396 478 498 516 538	-497002035196
STPT(10)	2725701007145661227	0 2 12 14 72 74 132 134 144 146	-490789616130
SPT(16)	2725701135331378961	0 12 32 42 80 92 96 198 290 392 396 408 446 456 476 488	-362603898396
SPT(16)	2725701232215609083	0 8 38 44 98 104 140 146 228 234 270 276 330 336 366 374	-265719668274
SPT(16)	2725701695498424887	0 6 14 26 30 32 116 132 164 180 264 266 270 282 290 296	197563147530
STPT(10)	2725701885485700941	0 2 30 32 120 122 210 212 240 242	387550423584
STPT(10)	2725702305098681717	0 2 12 14 42 44 72 74 84 86	807163404360
SPT(16)	2725702436593203653	0 6 14 60 84 98 108 126 158 176 186 200 224 270 278 284	938657926296
STPT(10)	2725702708998173657	0 2 30 32 42 44 54 56 84 86	1211062896300