I have a decent high school knowledge of Elementary Number Theory and it is also a subject I love to study. I have a good background in Real Analysis (not Complex Analysis) and Abstract Algbera. I have a strong foundation in Probability Theory and some knowledge of Measure Theory.
I would like to know an interesting introductory book for Probabilistic Number Theory (a subject completely new to me but looks tremendously appealing). Do I need knowledge about Analytic Number Theory and Algebraic Number Theory? If so, please mention which book to start with and then how to make transitions.
Also, what are the prerequisites for Algebraic, Analytic or Probabilistic Number Theory? I am a second year undergraduate in mathematics and statistics.