Landau's problems
four basic unsolved problems about prime numbers: Goldbach’s conjecture; twin prime conjecture; Legendre’s conjecture; whether there are infinitely many primes of the form 𝑛²+1
Landau's problems are four basic problems about prime numbers. They were listed at the 1912 International Congress of Mathematicians and presented by Edmund Landau.[1]
Problems change
These problems were presented in his speech as "unattackable at the present state of mathematics". They are as follows:
- Goldbach's conjecture: Can every even integer greater than 2 be written as the sum of two primes?
- Twin prime conjecture: Are there infinitely many primes p such that p + 2 is prime?
- Legendre's conjecture: Does there always exist at least one prime between consecutive perfect squares?
- 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 August 2022, all four problems are unresolved.
References change
- ↑ Weisstein, Eric W. "Landau's Problems". mathworld.wolfram.com. Retrieved 2022-08-27.
