Additive number theory is a branch of mathematics that focuses on the properties and relationships of numbers through addition. It studies how numbers can be expressed as sums of other numbers, often exploring questions about the existence of certain sums and the ways in which numbers can be combined. One of the key areas of interest in additive number theory is the study of prime numbers and their distribution. Researchers investigate problems such as the Goldbach conjecture, which posits that every even integer greater than two can be expressed as the sum of two prime numbers.