Landau's Problems

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Four problems about prime numbers posed by Edmund Landau in 1912, none of which are solved as of 2023:

  1. Goldbach's conjecture: Is every even integer (except 2) the sum of two primes?

  2. Twin prime conjecture: Are there infinitely many primes p such that p+2 is also prime?

  3. Legendre's conjecture: Is there always a prime between any two perfect squares?

  4. Are there infinitely many primes of the form n^2+1?

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