Prime p₀= 2068682791101656699 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 16 2 16 2 10 2 (?)
a_n: 0 2 12 14 30 32 48 50 60 62
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: 62
Found by: Cruncher Pete
db: batch=80, k=10, 2 10 2 16 2

STPT(10)	2068682124068027231	0 2 30 32 78 80 126 128 156 158	-667033629468
STPT(10)	2068682200382831777	0 2 42 44 72 74 102 104 144 146	-590718824922
SPT(16)	2068682346800610041	0 26 62 68 90 128 168 176 222 230 270 308 330 336 372 398	-444301046658
SPT(16)	2068682560657699319	0 2 20 62 72 90 98 138 344 384 392 410 420 462 480 482	-230443957380
SPT(16)	2068682631981646627	0 30 34 36 52 64 66 112 234 280 282 294 310 312 316 346	-159120010072
TPT(14)	2068682771478413087	0 2 30 32 54 56 60 62 90 92 132 134 174 176	-19623243612
SPT(16)	2068683291974068333	0 46 70 120 154 156 160 186 214 240 244 246 280 330 354 400	500872411634
SPT(16)	2068683413220372433	0 28 58 64 70 108 136 144 160 168 196 234 240 246 276 304	622118715734
STPT(10)	2068683537375678281	0 2 36 38 78 80 120 122 156 158	746274021582
SPT(16)	2068684184775514679	0 14 24 204 228 234 240 282 380 422 428 434 458 638 648 662	1393673857980
SPT(16)	2068684383912668293	0 16 18 30 46 48 136 148 156 168 256 258 274 286 288 304	1592811011594