Prime p₀= 3565552429821026069 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 24 26 18 10 6 6 32 28 32 6 6 10 18 26 24 (?)
a_n: 0 24 50 68 78 84 90 122 150 182 188 194 204 222 248 272
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: 272
Found by: [SG]KidDoesCrunch
db: batch=84, k=16, 24 26 18 10 6 6 32 28

SPT(16)	3565551000643357811	0 12 26 116 150 158 210 236 282 308 360 368 402 492 506 518	-1429177668258
SPT(16)	3565551171268725293	0 6 26 54 68 116 128 156 158 186 198 246 260 288 308 314	-1258552300776
STPT(10)	3565551370055329397	0 2 30 32 42 44 54 56 84 86	-1059765696672
SPT(16)	3565551599083821947	0 12 42 62 66 80 90 174 182 266 276 290 294 314 344 356	-830737204122
TPT(14)	3565551658266092951	0 2 30 32 126 128 150 152 210 212 276 278 288 290	-771554933118
TPT(14)	3565551684219451349	0 2 12 14 90 92 150 152 222 224 252 254 372 374	-745601574720
TPT(16)	3565553280985297517	0 2 12 14 102 104 144 146 180 182 222 224 312 314 324 326	851164271448
STPT(16)	3565553280985297517	0 2 12 14 102 104 144 146 180 182 222 224 312 314 324 326	851164271448
SPT(16)	3565553280985297517	0 2 12 14 102 104 144 146 180 182 222 224 312 314 324 326	851164271448
STPT(10)	3565553555369203751	0 2 78 80 108 110 138 140 216 218	1125548177682
STPT(12)	3565554141076349627	0 2 30 32 60 62 72 74 102 104 132 134	1711255323558