Near-square primes conjecture

In 1912, Edmund Landau listed four basic problems about prime numbers in the International Congress of Mathematicians. These problems are now known as Landau's problems. Landau's fourth problem asked whether there are infinitely many primes which are of the form $n^{2}+1$ for some integer $n$. This problem remains open and it is known as the Near-square primes conjecture. We prove this conjecture is indeed true.