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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.

Jack
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  • the problem is open. You want resources that contain partial progress? – leshik Jul 01 '14 at 03:44
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    There is a more general conjecture on the infinitude of prime outputs of certain polynomials : http://en.m.wikipedia.org/wiki/Bunyakovsky_conjecture – Yiyuan Lee Jul 01 '14 at 03:45
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    Look at this post http://math.stackexchange.com/questions/44126/primes-of-the-form-n21-hard The best partial progress for the polynomial values that are prime (in two dimensions though) is the work of Iwaniec and Friedlander http://en.wikipedia.org/wiki/Friedlander–Iwaniec_theorem – leshik Jul 01 '14 at 03:59
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    These primes are tabulated at https://oeis.org/A002496 and you might want to start by looking at some of the references and links on that page. – Gerry Myerson Jul 01 '14 at 05:28

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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.

Klangen
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