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The Bombieri-Vinogradov theorem for primes of the form $\mathbf{p=x^2+y^2+1}$

The Bombieri-Vinogradov theorem for primes of the form $\mathbf{p=x^2+y^2+1}$

In this paper, we establish a Bombieri-Vinogradov type result for prime numbers of the form $p=x^2+y^2+1$. The proof is based on the enveloping sieve.