Where can one find existing work on the following problem?
Prove there are infinitely many primes of the form $n^2 + 1$.
Resources about related work would also be appreciated.
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This is an open problem, considered very difficult with the current state of number theory. Landau posed this problem more than 100 years ago, and it still has no solution.
As others have pointed out in the comment section, this is a more general sub-problem of the Bunyakovsky conjecture.