What Are the Best Number Theory Books for Various Levels of Expertise?

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Suggestions for number theory references include "Prime Numbers: A Computational Perspective" by Carl Pomerance, which is highly regarded. Other recommended texts are "Number Theory for Computing" by Yan, "A Computational Introduction to Number Theory and Algebra" by Shoup, and "Number Theory with Computer Applications" by Kumanduri. Additionally, a notable German reference is "Algorithmische Zahlentheorie" by Forster, though it may be harder to find. These resources cater to those with a foundational understanding of elementary number theory and algebra, offering insights into computational aspects of the field.
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Does anyone have suggestions for number theory references? I'm already familiar with elementary number theory and have some algebra background, but I'm not sure what kind of number theory I'm interested in yet. Thanks!
 
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Prime Numbers a Computational Perspective
by Carl Pomerance

is one of the best.
 
Yan: Number Theory for Computing
Shoup: A Computational Introduction to Number Theory and Algebra
Kumanduri: Number Theory with Computer Applications
Hard to find an written in German:
Forster: Algorithmische Zahlentheorie
 

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