Learning Program Synthesis for Integer Sequences from Scratch

The search for abstract patterns is one of the principal occupations of mathematicians. The discovery of similar patterns across different mathematical fields often leads to surprising connections. Probably the most famous example of such an unexpected connection in mathematics is the Taniyama-Shimura conjecture proved in 2001 [2]. It relates elliptic curves over the field of rational numbers with a special kind of complex analytical functions known as modular forms. This conjecture became especially famous because a restricted version of it implies Fermat's last theorem [16]. The connections found by the system described in this paper are more modest. For instance, it has created formulas for testing prime numbers based both on Fermat's little theorem