A slightly various form of Dirichlet's theorem on arithmetic progressions

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Are there infinitely many primes of the form $2n(n+1)+1$?

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This is a completely open question; see http://en.wikipedia.org/wiki/Ulam_spiral#Hardy_and_Littlewood.27s_Conjecture_F if you are interested in some background, and a link to the more general Bunyakovsky's conjecture.