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Although many efforts have been made through past years, skin cancer recognition from medical images is still an active area of research aiming at more accurate results. Many efforts have been made in recent years based on deep learning neural networks. Only a few, however, are based on a single deep learning model and targeted to create a mobile application. Contributing to both efforts, first we present a summary of the required medical knowledge on skin cancer, followed by an extensive summary of the most recent related works. Afterwards, we present 11 CNN (convolutional neural network) candidate single architectures. We train and test those 11 CNN architectures, using the HAM10000 dataset, concerning seven skin lesion classes. To face the imbalance problem and the high similarity between images of some skin lesions, we apply data augmentation (during training), transfer learning and fine-tuning. From the 11 CNN architecture configurations, DenseNet169 produced the best results. It achieved an accuracy of 92.25%, a recall (sensitivity) of 93.59% and an F1-score of 93.27%, which outperforms existing state-of-the-art efforts. We used a light version of DenseNet169 in constructing a mobile android application, which was mapped as a two-class model (benign or malignant). A picture is taken via the mobile device camera, and after manual cropping, it is classified into benign or malignant type. The application can also inform the user about the allowed sun exposition time based on the current UV radiation degree, the phototype of the user’s skin and the degree of the used sunscreen. In conclusion, we achieved state-of-the-art results in skin cancer recognition based on a single, relatively light deep learning model, which we also used in a mobile application.