The Pipe nebula is a massive, nearby, filamentary dark molecular cloud with a low star-formation efficiency threaded by a uniform magnetic field perpendicular to its main axis. It harbors more than a hundred, mostly quiescent, very chemically young starless cores. The cloud is, therefore, a good laboratory to study the earliest stages of the star-formation process. We aim to investigate the primordial conditions and the relation among physical, chemical, and magnetic properties in the evolution of low-mass starless cores. We used the IRAM 30-m telescope to map the 1.2 mm dust continuum emission of five new starless cores, which are in good agreement with previous visual extinction maps. For the sample of nine cores, which includes the four cores studied in a previous work, we derived a Av to NH2 factor of (1.27$pm$0.12)$times10^{-21}$ mag cm$^{2}$ and a background visual extinction of ~6.7 mag possibly arising from the cloud material. We derived an average core diameter of ~0.08 pc, density of ~10$^5$ cm$^{-3}$, and mass of ~1.7 Msun. Several trends seem to exist related to increasing core density: (i) diameter seems to shrink, (ii) mass seems to increase, and (iii) chemistry tends to be richer. No correlation is found between the direction of the surrounding diffuse medium magnetic field and the projected orientation of the cores, suggesting that large scale magnetic fields seem to play a secondary role in shaping the cores. The full abstract is available in the pdf.
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