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The stellar initial mass function (IMF) is critical to our understanding of star formation and the effects of young stars on their environment. On large scales, it enables us to use tracers such as UV or Hα emission to estimate the star formation rate of a system and interpret unresolved star clusters across the Universe. So far, there is little firm evidence of large-scale variations of the IMF, which is thus generally considered “universal”. Stars form from cores, and it is now possible to estimate core masses and compare the core mass function (CMF) with the IMF, which it presumably produces. The goal of the ALMA-IMF large programme is to measure the core mass function at high linear resolution (2700 au) in 15 typical Milky Way protoclusters spanning a mass range of 2.5 × 10³to 32.7 × 10³M_⊙. In this work, we used two different core extraction algorithms to extract ≈680 gravitationally bound cores from these 15 protoclusters. We adopted a per core temperature using the temperature estimate from the point-process mapping Bayesian method (PPMAP). A power-law fit to the CMF of the sub-sample of cores above the 1.64M_⊙completeness limit (330 cores) through the maximum likelihood estimate technique yields a slope of 1.97 ± 0.06, which is significantly flatter than the 2.35 Salpeter slope. Assuming a self-similar mapping between the CMF and the IMF, this result implies that these 15 high-mass protoclusters will generate atypical IMFs. This sample currently is the largest sample that was produced and analysed self-consistently, derived at matched physical resolution, with per core temperature estimates, and cores as massive as 150M_⊙. We provide both the raw source extraction catalogues and the catalogues listing the source size, temperature, mass, spectral indices, and so on in the 15 protoclusters.