The main question advanced in this paper is as follows: Which specific criterion is used to distinguish the problems of prime philosophy from each other. Another related question here is whether Islamic philosophers really employ this criterion or not. A review of the works of Greek philosophers, particularly Aristotle, indicates that Aristotle’s words regarding the subject of prime philosophy are diverse and divided. It also reveals that the problems of prime philosophy have not been inferred and formulated with reference to a specific subject in an organized manner. In spite of the entrance of Greek philosophy and all its concomitants into the world of Islam, Islamic philosophers, especially Ibn Sina, tried to explain the subject of prime philosophy and its problems, dissect the relationship between them, and provide a criterion for distinguishing philosophical problems from the problems of other sciences. They often considered the subject of prime philosophy to be existent qua existent and assumed that its problems include predicates which are deemed to be among the essential accidents of pure existents. Therefore, the main criterion for identifying the problems of prime philosophy and distinguishing them from each other was introduced as follows: the predicates of those problems had to be essential accidents for absolute existents. Nevertheless, in reality, these philosophers discussed some problems the predicates of which did not follow this rule. A study of the works of Aristotle and Islamic philosophers reveals that the secret of this ambiguity is hidden in an approach according to which they firstly divided theoretical sciences into three categories: natural sciences, mathematics, and prime philosophy. Then, in reality, they transferred the problems that could not be discussed in the other two sciences to the domain of prime philosophy while the equivalence of their predicates with essential accidents for existent qua existent were questionable. The present paper aims to analyze and explain the above claims in detail based on reliable documents and arguments and disclose the main reason behind the lack of conformity between the problems and the subject of prime philosophy in the history of Islamic philosophy.