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Estimating the primary quantization matrix of double JPEG compressed images is a problem of relevant importance in image forensics since it allows to infer important information about the past history of an image. In addition, the inconsistencies of the primary quantization matrices across different image regions can be used to localize splicing in double JPEG tampered images. Traditional model-based approaches work under specific assumptions on the relationship between the first and second compression qualities and on the alignment of the JPEG grid. Recently, a deep learning-based estimator capable to work under a wide variety of conditions has been proposed, that outperforms tailored existing methods in most of the cases. The method is based on a Convolutional Neural Network (CNN) that is trained to solve the estimation as a standard regression problem. By exploiting the integer nature of the quantization coefficients, in this paper, we propose a deep learning technique that performs the estimation by resorting to a simil-classification architecture. The CNN is trained with a loss function that takes into account both the accuracy and the Mean Square Error (MSE) of the estimation. Results confirm the superior performance of the proposed technique, compared to the state-of-the art methods based on statistical analysis and, in particular, deep learning regression. Moreover, the capability of the method to work under general operative conditions, regarding the alignment of the second compression grid with the one of first compression and the combinations of the JPEG qualities of former and second compression, is very relevant in practical applications, where these information are unknown a priori.