Analytic Number Theory by Andrew Granville.

Gaps Between Primes Revisited.

Sieve Methods.

Smooth Numbers.

Interesting scientific or quantitative thoughts or ideas!

Analytic Number Theory by Andrew Granville.

Gaps Between Primes Revisited.

Sieve Methods.

Smooth Numbers.

Analytic Number Theory by Andrew Granville.

Gaps Between Primes that are Smaller than Average.

Very Small Gaps Between Primes.

Analytic Number Theory by Andrew Granville.

The “analysis” in analytic number theory.

The Riemann hypothesis. If 0<=Re(s)<=1, s complex and Zeta(s) = 0 then Re(s)=1/2.

Primes in arithmetic progressions.

Primes in short intervals.

Analytic Number Theory by Andrew Granville.

Various proofs that there are an infinite number of primes.

Bounds for the number of primes.

Algebraic Numbers by Barry Mazur.

Fields of Algebraic Numbers.

Rings of Algebraic Integers.

On the size(s) of the absolute values of all conjugates of an algebraic integer.

Weil Numbers.

Epilogue.

IV.2 Analytic Number Theory by Andrew Granville.

Introduction.

Analytic number theory, as opposed to algebraic, looks for good approximations.

Algebraic Numbers by Barry Mazur.

The degree of an algebraic number.

Algebraic numbers as ciphers determined by their minimal polynomials.

A few remarks about the theory of polynomials.