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Arithmetic progressions of three prime numbers with two primes of the form $\mathbf{p=x^2+y^2+1}$
Published 13 Oct 2016 in math.NT | (1610.04044v6)
Abstract: In the present paper we prove that there exist infinitely many arithmetic progressions of three different primes $p_1,p_2,p_3=2p_2-p_1$ such that $p_1=x_12 + y_12 +1$, $p_2=x_22 + y_22 +1$.
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