Prime p₀= 4506179043011152307 starts a Symmetric tuple of 13 consecutive primes (SPT).
d_n: 0 36 30 54 30 30 126 126 30 30 54 30 36 (?)
a_n: 0 36 66 120 150 180 306 432 462 492 546 576 612
All 13 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 612
Found by: [SG]KidDoesCrunch
db: batch=85, k=13, 36 30 54 30 30 126

STPT(10)	4506177643301724359	0 2 12 14 30 32 48 50 60 62	-1399709427948
SPT(16)	4506177794270192627	0 12 42 66 74 116 144 164 252 272 300 342 350 374 404 416	-1248740959680
STPT(10)	4506178046372409917	0 2 42 44 72 74 102 104 144 146	-996638742390
TPT(14)	4506178279877500199	0 2 30 32 72 74 78 80 150 152 252 254 288 290	-763133652108
STPT(10)	4506178308044722277	0 2 90 92 150 152 210 212 300 302	-734966430030
SPT(16)	4506178828444766027	0 14 42 44 60 62 86 92 114 120 144 146 162 164 192 206	-214566386280
SPT(16)	4506180325787241371	0 26 50 62 72 86 90 132 140 182 186 200 210 222 246 272	1282776089064
SPT(16)	4506180773346401771	0 48 62 72 108 138 150 152 186 188 200 230 266 276 290 338	1730335249464
STPT(10)	4506180875121096947	0 2 12 14 42 44 72 74 84 86	1832109944640
TPT(14)	4506181367404378307	0 2 120 122 174 176 252 254 282 284 312 314 384 386	2324393226000
SPT(16)	4506181397152290227	0 14 80 110 126 144 150 176 210 236 242 260 276 306 372 386	2354141137920