Prime p₀= 346240490795548343 starts a Symmetric tuple of 14 consecutive primes (SPT).
d_n: 0 8 6 12 28 2 4 14 4 2 28 12 6 8 (?)
a_n: 0 8 14 26 54 56 60 74 78 80 108 120 126 134
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 134
Found by: Cruncher Pete
db: batch=70, k=14, 8 6 12 28 2 4 14

SPT(16)	346240470783963761	0 68 78 80 110 120 126 168 218 260 266 276 306 308 318 386	-20011584582
TPT(12)	346240475555066537	0 2 84 86 102 104 210 212 264 266 282 284	-15240481806
SPT(14)	346240479749472901	0 66 88 102 112 162 192 376 406 456 466 480 502 568	-11046075442
STPT(10)	346240480046547131	0 2 36 38 108 110 180 182 216 218	-10749001212
SPT(14)	346240480640089307	0 72 84 90 140 206 210 236 240 306 356 362 374 446	-10155459036
SPT(16)	346240488732897989	0 60 68 72 90 102 110 114 128 132 140 152 170 174 182 242	-2062650354
SPT(14)	346240497496895077	0 46 52 112 136 180 196 240 256 300 324 384 390 436	6701346734
SPT(14)	346240507457196991	0 46 60 88 100 126 148 168 190 216 228 256 270 316	16661648648
SPT(14)	346240515006524431	0 16 42 52 82 90 100 108 118 126 156 166 192 208	24210976088
SPT(14)	346240518198674251	0 42 48 130 132 136 148 150 162 166 168 250 256 298	27403125908
TPT(12)	346240520883369821	0 2 18 20 36 38 78 80 90 92 228 230	30087821478