Landau’s problems
Landau’s problems are four conjectures about prime numbers^{} which were unsolved at the time Edmund Landau presented on them at International Congress of Mathematicians of 1912.

1.
Goldbach’s conjecture

2.
The twin prime conjecture^{}

3.
Legendre’s conjecture

4.
The conjecture that there are infinitely many primes of the form $p={n}^{2}+1$.
Unlike similar collections of unsolved problems, this collection does not include the Riemann hypothesis^{}.
Almost a hundred years later, all four of Landau’s problems are still unsolved.
Title  Landau’s problems 

Canonical name  LandausProblems 
Date of creation  20130322 16:38:25 
Last modified on  20130322 16:38:25 
Owner  PrimeFan (13766) 
Last modified by  PrimeFan (13766) 
Numerical id  4 
Author  PrimeFan (13766) 
Entry type  Definition 
Classification  msc 01A60 