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The molecule studied in this work, 2-hydroxyprop-2-enal, is among the candidates to be searched for in the interstellar medium (ISM), as it is a dehydration product of C3 sugars and contains structural motifs typical for some interstellar molecules. The aim of this work is to deepen knowledge about the millimetre-wave spectrum of 2-hydroxyprop-2-enal in the region enabling its search towards astronomical objects. We target the solar-type protostar IRAS16293-2422 and star-forming region Sagittarius (Sgr) B2(N). The rotational spectrum of 2-hydroxyprop-2-enal was measured and analysed in the frequency regions of 128-166 GHz and 285-329 GHz. The interstellar exploration towards IRAS16293-2422 was based on the Atacama Large Millimeter/submillimeter Array (ALMA) data of the Protostellar Interferometric Line Survey. We also used the imaging spectral line survey ReMoCA performed with ALMA toward Sgr B2(N). We modelled the astronomical spectra under the assumption of local thermodynamic equilibrium. We provide analysis of hundreds of rotational transitions of 2-hydroxyprop-2-enal in the ground state and the lowest lying excited vibrational state. We report its nondetection towards IRAS16293 B. The 2-hydroxyprop-2-enal/3-hydroxypropenal abundance ratio is estimated to be less-than or similar to 0.9-1.3 in agreement with the predicted value of 1.4. We also report the nondetection of 2-hydroxyprop-2-enal toward the hot molecular core Sgr B2(N1). We did not detect the related aldehydes 2-hydroxypropanal and 3-hydroxypropenal either. We find that these three molecules are at least 9, 4, and 10 times less abundant than acetaldehyde in this source, respectively. Despite the nondetections, the results of this work represent a significant improvement on previous investigations in the microwave region and meets the requirements for further searches of this molecule in the ISM.