Prime number races

Abstract

Translator's abstractThis paper deals with one of the important and interesting topics in Number Theory under the title of prime number races, which is less discussed in Persian texts. All prime numbers (except 2) can be written in the form 4n+1 or 4n+3. The question that naturally arises is, which category contains more prime numbers? Certainly, the infinity of prime numbers makes it difficult for the spectator to predict the competition. The present article, which was written by two prominent mathematicians in this field, has comprehensively discussed the history of this problem, the types of prime number races, and the research work done in this field