Titlebook: Steps into Analytic Number Theory; A Problem-Based Intr Paul Pollack,Akash Singha Roy Textbook 2021 The Editor(s) (if applicable) and The A

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Step #2,Asymptotic estimates related to .(.). Many proofs that there are infinitely many primes. The Principle of Inclusion-Exclusion enters the picture.

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Step #3,The Euler product representation, logarithm, and reciprocal of .(.). The Jordan–Bonferroni inequalities. Upper and lower bounds for the divisor-counting function .(.).

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Step #9,The probability a random integer is squarefree. Brun’s upper bound on the count of twin primes and the convergence of ∑.1∕.. Existence of a nonsquare modulo . that is ., for all large ..

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Step #10,Mertens’ estimate for ∑.1∕.. How many prime factors an integer has, on average. A recursive formula for .(2.). First musings on primitive prime factors of 2. − 1.