# Landau'S Problems

Tech

## What is Landau's problems?

At the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime numbers. These problems were characterised in his speech as "unattackable at the present state of mathematics" and are now known as Landau's problems. They are as follows: 1. * Goldbach's conjecture: Can every even integer greater than 2 be written as the sum of two primes? 2. * Twin prime conjecture: Are there infinitely many primes p such that p + 2 is prime? 3. * Legendre's conjecture: Does there always exist at least one prime between consecutive perfect squares? 4. * Are there infinitely many primes p such that p − 1 is a perfect square? In other words: Are there infinitely many primes of the form n2 + 1? As of June 2020, all four problems are unresolved.

### Technology Types

conditionconjectureconjectures about prime numberdefinite quantitydifficultyhypothesisprimeprime numberproblemspeculationunsolved problems in mathematic

### Synonyms

Landau conjecturesLandau problemsLandau's conjecturesNear-square primes

### Translations

Landau-Probleme (de)Landauren problemak (eu)Landaus problem (sv)Problemas de Landau (es)Problemas de Landau (pt)Problemen van Landau (nl)Problemes de Landau (ca)Problèmes de Landau (fr)Problemi di Landau (it)Проблеми Ландау (uk)Проблемы Ландау (ru)معضلات لاندو (ar)兰道问题 (zh)

## Tech Info

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