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We would like to thank the Instituto de Astrofísica de Canarias for the excellent working conditions at the Observatorio del Roque de los Muchachos in La Palma. The financial support of the German BMBF and MPG, the Italian INFN and INAF, the Swiss National Fund SNF, the ERDF under the Spanish MINECO (FPA2012-39502), and the Japanese JSPS and MEXT is gratefully acknowledged. This work was also supported by the Centro de Excelencia Severo Ochoa SEV-2012-0234, CPAN CSD2007-00042, and MultiDark CSD2009-00064 projects of the Spanish Consolider-Ingenio 2010 programme, by grant 268740 of the Academy of Finland, by the Croatian Science Foundation (HrZZ) Project 09/176 and the University of Rijeka Project 13.12.1.3.02, by the DFG Collaborative Research Centers SFB823/C4 and SFB876/C3, and by the Polish MNiSzW grant 745/N-HESSMAGIC/2010/0.Aims. We investigate the extension of the very high-energy spectral tail of the Crab Pulsar at energies above 400 GeV. Methods. We analyzed ~320 h of good-quality Crab data obtained with the MAGIC telescope from February 2007 to April 2014. Results. We report the most energetic pulsed emission ever detected from the Crab Pulsar reaching up to 1.5 TeV. The pulse profile shows two narrow peaks synchronized with those measured in the GeV energy range. The spectra of the two peaks follow two different power-law functions from 70 GeV up to 1.5 TeV and connect smoothly with the spectra measured above 10 GeV by the Large Area Telescope (LAT) on board the Fermi satellite. When making a joint fit of the LAT and MAGIC data above 10 GeV the photon indices of the spectra differ by 0.5 ± 0.1. Conclusions. Using data from the MAGIC telescopes we measured the most energetic pulsed photons from a pulsar to date. Such TeV pulsed photons require a parent population of electrons with a Lorentz factor of at least 5 × 106. These results strongly suggest IC scattering off low-energy photons as the emission mechanism and a gamma-ray production region in the vicinity of the light cylinder.engjournal articlehttp://dx.doi.org/10.1051/0004-6361/201526853http://www.aanda.org/open access537539.1Gamma-ray pulsarsHigh-energy emissionOuter gap modelMajor upgradeSlot gapsTelescopeRadiationSpectraNebulaAcceleration.ElectricidadElectrónica (Física)Física nuclear2202.03 Electricidad2207 Física Atómica y Nuclear