Prime p₀= 4506357808424365769 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 74 10 36 20 4 56 10 8 10 56 4 20 36 10 74 (?)
a_n: 0 74 84 120 140 144 200 210 218 228 284 288 308 344 354 428
All 16 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 428
Found by: [SG]KidDoesCrunch
db: batch=85, k=16, 74 10 36 20 4 56 10 8

STPT(10)	4506354446221976399	0 2 18 20 30 32 42 44 60 62	-3362202389370
STPT(10)	4506355057397781197	0 2 30 32 42 44 54 56 84 86	-2751026584572
SPT(16)	4506355277196801629	0 2 14 24 42 60 90 102 152 164 194 212 230 240 252 254	-2531227564140
SPT(18)	4506355841925853717	0 90 114 132 154 180 214 216 222 244 250 252 286 312 334 352 376 466	-1966498512052
SPT(16)	4506356355325716107	0 2 12 54 56 80 86 144 152 210 216 240 242 284 294 296	-1453098649662
STPT(10)	4506357375335350289	0 2 18 20 30 32 42 44 60 62	-433089015480
STPT(10)	4506357841527701309	0 2 132 134 150 152 168 170 300 302	33103335540
SPT(16)	4506358336262505451	0 16 40 82 108 180 190 192 196 198 208 280 306 348 372 388	527838139682
SPT(16)	4506358867683297277	0 46 60 66 70 132 142 162 184 204 214 276 280 286 300 346	1059258931508
TPT(14)	4506358870592902241	0 2 78 80 90 92 120 122 156 158 228 230 240 242	1062168536472
TPT(14)	4506358898640902579	0 2 12 14 42 44 48 50 78 80 132 134 150 152	1090216536810