| Summary: | <p>Production cross-sections of prompt charm mesons are measured with the first data from <i>pp</i> collisions at the LHC at a centre-of-mass energy of 13 TeV. The data sample corresponds to an integrated luminosity of 4.98 ± 0.19 pb<sup>−1</sup> collected by the LHCb experiment. The production cross-sections of <i>D</i><sup>0</sup>, <i>D</i><sup>+</sup>, <i>D</i><sub><i>s</i></sub><sup>+</sup>, and <i>D</i><sup>*+</sup> mesons are measured in bins of charm meson transverse momentum, <i>p</i><sub>T</sub>, and rapidity, <i>y</i>, and cover the range 0 < <i>p</i><sub>T</sub> < 15GeV/c and 2.0 < <i>y</i> < 4.5. The inclusive cross-sections for the four mesons, including charge conjugation, within the range of 1 < <i>p</i><sub>T</sub> < 8 GeV/c are found to be<br/> <i>σ</i>(<i>pp</i> →<i>D</i><sup>0</sup><i>X</i>) = 2460 ± 3 ± 130 <i>μ</i>b<br/> <i>σ</i>(<i>pp</i> →<i>D</i><sup>+</sup><i>X</i>) = 1000 ± 3 ± 110 <i>μ</i>b<br/> <i>σ</i>(<i>pp</i> →<i>D</i><sup>+</sup><sub><i>s</i></sub><i>X</i>) = 460 ± 13 ± 100 <i>μ</i>b<br/> <i>σ</i>(<i>pp</i> →<i>D</i><sup>∗+</sup><i>X</i>)=880 ± 5 ± 140 <i>μ</i>b<br/> where the uncertainties are due to statistical and systematic uncertainties, respectively.</p>
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