In this paper we improve the result of Akbary and Hambrook by a factor of log x by obtaining a better version of Vaughan's inequality and using the explicit variant of an inequality connected to the M\"obius function, derived by Helfgott in his work on ternary Goldbach conjecture.
A variant of the Bombieri-Vinogradov theorem with explicit constants and applications
The Bombieri-Vinogradov theorem for primes of the form $\mathbf{p=x^2+y^2+1}$
The ternary Goldbach conjecture is true
![QR code for arXiv:1610.05344 [math.NT]](http://oss.arxitics.com/images/favicon.svg)