Prime p₀= 4401788618218702817 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: [SG]KidDoesCrunch
db: batch=85, k=10, 2 10 2 28 2

SPT(16)	4401787110346627087	0 4 16 22 30 34 52 64 72 84 102 106 114 120 132 136	-1507872075730
TPT(14)	4401787359800851451	0 2 6 8 60 62 138 140 186 188 210 212 300 302	-1258417851366
STPT(10)	4401787521038956439	0 2 138 140 180 182 222 224 360 362	-1097179746378
TPT(14)	4401788060180099051	0 2 36 38 66 68 150 152 180 182 288 290 306 308	-558038603766
STPT(10)	4401788367000999851	0 2 30 32 60 62 90 92 120 122	-251217702966
STPT(10)	4401788481315695999	0 2 42 44 90 92 138 140 180 182	-136903006818
SPT(22)	4401788827290865187	0 14 72 84 176 182 206 212 224 392 396 440 444 612 624 630 654 660 752 764 822 836	209072162370
STPT(10)	4401788849772634079	0 2 42 44 90 92 138 140 180 182	231553931262
SPT(16)	4401789163834883621	0 8 78 98 110 140 150 152 348 350 360 390 402 422 492 500	545616180804
SPT(16)	4401789622232773481	0 6 20 50 78 90 96 132 146 182 188 200 228 258 272 278	1004014070664
SPT(16)	4401790132276626491	0 12 36 56 72 90 140 182 246 288 338 356 372 392 416 428	1514057923674