Prime p₀= 4387610549906124599 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 40 2 16 2 16 2 40 2 (?)
a_n: 0 2 42 44 60 62 78 80 120 122
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: 122
Found by: [SG]KidDoesCrunch
db: batch=85, k=10, 2 40 2 16 2

STPT(10)	4387607480827032557	0 2 30 32 42 44 54 56 84 86	-3069079092042
SPT(16)	4387607711950919207	0 36 56 86 170 204 264 306 404 446 506 540 624 654 674 710	-2837955205392
STPT(10)	4387607745736758857	0 2 30 32 72 74 114 116 144 146	-2804169365742
SPT(16)	4387608680308509589	0 40 82 120 142 148 174 204 238 268 294 300 322 360 402 442	-1869597615010
TPT(14)	4387608854945895881	0 2 66 68 78 80 156 158 198 200 240 242 288 290	-1694960228718
STPT(10)	4387608881934863831	0 2 36 38 138 140 240 242 276 278	-1667971260768
STPT(10)	4387610695888049657	0 2 30 32 42 44 54 56 84 86	145981925058
STPT(10)	4387610734708349189	0 2 18 20 30 32 42 44 60 62	184802224590
TPT(14)	4387610810020965251	0 2 48 50 60 62 90 92 126 128 156 158 168 170	260114840652
STPT(12)	4387610810020965299	0 2 12 14 42 44 78 80 108 110 120 122	260114840700
SPT(16)	4387610869758928157	0 54 84 90 104 120 132 192 194 254 266 282 296 302 332 386	319852803558