Prime p₀= 1123364000260247623 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 54 10 6 30 26 28 26 40 26 28 26 30 6 10 54 (?)
a_n: 0 54 64 70 100 126 154 180 220 246 274 300 330 336 346 400
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: 400
Found by: crashtech
db: batch=76, k=16, 54 10 6 30 26 28 26 40

SPT(16)	1123362434543993299	0 10 18 88 108 120 160 172 210 222 262 274 294 364 372 382	-1565716254324
STPT(10)	1123362749003094527	0 2 12 14 72 74 132 134 144 146	-1251257153096
SPT(16)	1123362991333298483	0 14 20 54 60 80 104 108 176 180 204 224 230 264 270 284	-1008926949140
STPT(10)	1123363638471483749	0 2 18 20 30 32 42 44 60 62	-361788763874
STPT(10)	1123363661416155371	0 2 36 38 78 80 120 122 156 158	-338844092252
SPT(16)	1123363878521848877	0 84 90 96 102 114 132 146 210 224 242 254 260 266 272 356	-121738398746
STPT(10)	1123364178981061481	0 2 36 38 78 80 120 122 156 158	178720813858
SPT(16)	1123365189482528593	0 24 34 66 100 108 138 154 240 256 286 294 328 360 370 394	1189222280970
SPT(16)	1123365263938989419	0 8 12 14 50 90 98 102 140 144 152 192 228 230 234 242	1263678741796
SPT(16)	1123365265396126607	0 2 60 110 116 156 162 182 264 284 290 330 336 386 444 446	1265135878984
STPT(10)	1123365373167433679	0 2 48 50 90 92 132 134 180 182	1372907186056