  Judging whether an integer can be divided by prime numbers such as 2 or 3 may
appear trivial to human beings, but can be less straightforward for computers.
Here, we tested multiple deep learning architectures and feature engineering
approaches on classifying integers based on their residues when divided by
small prime numbers. We found that the ability of classification critically
depends on the feature space. We also evaluated Automated Machine Learning
(AutoML) platforms from Amazon, Google and Microsoft, and found that they
failed on this task without appropriately engineered features. Furthermore, we
introduced a method that utilizes linear regression on Fourier series basis
vectors, and demonstrated its effectiveness. Finally, we evaluated Large
Language Models (LLMs) such as GPT-4, GPT-J, LLaMA and Falcon, and demonstrated
their failures. In conclusion, feature engineering remains an important task to
improve performance and increase interpretability of machine-learning models,
even in the era of AutoML and LLMs.
