This is a list of number theory topics, by Wikipedia page. See also list of cryptology topics.

Table of contents
1 Factors
2 Modular arithmetic
3 Primality tests and factorization
4 Arithmetic functions
5 Analytic number theory: additive problems
6 Algebraic number theory
7 Quadratic forms
8 L-functions
9 Diophantine equations
10 Diophantine approximation
11 Named primes
12 Pseudo-random numbers
13 Recreational topics

Factors

Modular arithmetic

Primality tests and factorization

Arithmetic functions

Analytic number theory: additive problems

Algebraic number theory

Quadratic forms

L-functions

Diophantine equations

Diophantine approximation

Named primes

Pseudo-random numbers

Recreational topics

NB Listing here is not perjorative, since many famous topics in number theory have origins in challenging problems posed purely for their own sake. See recreational mathematics.