Search for primes of the form m²+1
Wolf, Marek
Original · EN
The results of the computer hunt for the primes of the form q = m²+1 up to 10²⁰ are reported. The number of sign changes of the difference πq(x) - Cq/2∫₂ˣdu √u(u) and the error term for this difference is investigated. The analogs of the Brun's constant and the Skewes number are calculated. An analog of the B conjecture of Hardy--Littlewood is formulated. It is argued that there is no Chebyshev bias for primes of the form q=m²+1. All encountered integrals we were able to express by the logarithmic integral.
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