Goldbach conjecture is one of the most famous open mathematical problems. It states that every even number, bigger than two, can be presented as a sum of 2 prime numbers. In this work we present a deep learning based model that predicts the number of Goldbach partitions for a given even number. Surprisingly, our model outperforms all state-of-the-art analytically derived estimations for the number of couples, while not requiring prime factorization of the given number. We believe that building a model that can accurately predict the number of couples brings us one step closer to solving one of the world most famous open problems. To the best of our knowledge, this is the first attempt to consider machine learning based data-driven methods to approximate open mathematical problems in the field of number theory, and hope that this work will encourage such attempts.
Among the dreams of mankind is the one dealing with the mecha nization of human thought. As the world today has become so complex that humans apparently fail to manage it properly with their intellectual gifts, the realization of this dream might be regarded even as something like a necessity. On the other hand, the incredible advances in computer technology let it appear as a real possibility. Of course, it is not easy to say what sort of thing human thinking actually is, a theme which over the centuries occupied many thinkers, mainly philosophers. From a critical point of view most of their theories were of a speculative nature since their only way of testing was by Gedanken-experi ments. It is the computer which has opened here a wide range of new possibilities since with this tool we now can model real experiments and thus test such theories like physicists do in their field. About a quarter of a century ago, scientific activi ties of that sort were started under the label of artificial intelligence Today these activities establish a wide and prosperous field which the author, in lack of any better name, prefers to call intellectics. Without any doubt, the com puter programs developed in this field have tought us much about the nature of human thinking.  In this paper we describe a complex information processing system, which we call the logic theory machine, that is capable of discovering proofs for theorems in symbolic logic. This system, in contrast to the systematic algorithms that are ordinarily employed in computation, relies heavily on heuristic methods similar to those that have been observed in . human problem solving activity. The specification is written in a formal language, of the nature of a pseudo-code, that is suitable for coding for digital computers. However, the present paper is concerned exclusively with specification of the system, and not with its realization in a computer. The logic theory machine is part of a program of research to understand complex information processing systems by specifying and synthesizing a substantial variety of such systems for empirical study.