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I had read basic number theory and also I had solved many problems in number theory. To widen my knowledge I want to explore more number theory. I am interested in conjectures like bertrand conjecture, goldbach conjecture. I also like to study the infinitude of primes in an arithmetic progressions. I want some guidance in this. Which books should I read to know more about such amazing properties. Thanks

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I believe you should read the two following books:

  1. Topics in the theory of numbers by Erdos and Suranyi (You will enjoy most of the book)

  2. Introduction to Analytic Number Theory by Tom Apostol (You will learn lots of stuff).