Prime p₀= 2566548959904768731 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 4 2 40 2 40 2 4 2 (?)
a_n: 0 2 6 8 48 50 90 92 96 98
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: 98
Found by: Ben
db: batch=82, k=10, 2 4 2 40 2

TPT(14)	2566546917391604417	0 2 12 14 54 56 90 92 114 116 180 182 210 212	-2042513164314
SPT(16)	2566547156104931011	0 48 78 90 112 136 138 160 168 190 192 216 238 250 280 328	-1803799837720
STPT(10)	2566547465408875307	0 2 60 62 102 104 144 146 204 206	-1494495893424
TPT(14)	2566547533684101659	0 2 102 104 108 110 150 152 180 182 198 200 222 224	-1426220667072
SPT(16)	2566548074931670307	0 36 86 150 170 186 192 230 312 350 356 372 392 456 506 542	-884973098424
STPT(10)	2566548133135477259	0 2 18 20 30 32 42 44 60 62	-826769291472
SPT(18)	2566549326478514483	0 18 54 74 78 84 138 156 170 234 248 266 320 326 330 350 386 404	366573745752
SPT(16)	2566549360777287323	0 6 78 138 176 218 230 320 324 414 426 468 506 566 638 644	400872518592
SPT(16)	2566549861892862949	0 28 48 64 88 90 178 190 192 204 292 294 318 334 354 382	901988094218
SPT(16)	2566550033721217919	0 14 30 42 72 102 104 140 144 180 182 212 242 254 270 284	1073816449188
STPT(10)	2566550309429366957	0 2 54 56 72 74 90 92 144 146	1349524598226