Prime p₀= 4506178308044722277 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 88 2 58 2 58 2 88 2 (?)
a_n: 0 2 90 92 150 152 210 212 300 302
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: 302
Found by: [SG]KidDoesCrunch
db: batch=85, k=10, 2 88 2 58 2

SPT(16)	4506177455676682129	0 4 18 24 54 58 70 84 238 252 264 268 298 304 318 322	-852368040148
STPT(10)	4506177555146461487	0 2 42 44 72 74 102 104 144 146	-752898260790
STPT(10)	4506177643301724359	0 2 12 14 30 32 48 50 60 62	-664742997918
SPT(16)	4506177794270192627	0 12 42 66 74 116 144 164 252 272 300 342 350 374 404 416	-513774529650
STPT(10)	4506178046372409917	0 2 42 44 72 74 102 104 144 146	-261672312360
TPT(14)	4506178279877500199	0 2 30 32 72 74 78 80 150 152 252 254 288 290	-28167222078
SPT(16)	4506178828444766027	0 14 42 44 60 62 86 92 114 120 144 146 162 164 192 206	520400043750
SPT(13)	4506179043011152307	0 36 66 120 150 180 306 432 462 492 546 576 612	734966430030
SPT(16)	4506180325787241371	0 26 50 62 72 86 90 132 140 182 186 200 210 222 246 272	2017742519094
SPT(16)	4506180773346401771	0 48 62 72 108 138 150 152 186 188 200 230 266 276 290 338	2465301679494
STPT(10)	4506180875121096947	0 2 12 14 42 44 72 74 84 86	2567076374670