Search for primes of the form m 2 + 1
نویسنده
چکیده
The results of the computer hunt for the primes of the form q = m + 1 up to 10 are reported. The number of sign changes of the difference πq(x) − Cq 2 ∫ x 2 du √ u log(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 = m + 1. All encountered integrals we were able to express by the logarithmic integral. Mathematics Subject Classification: 11L20, 11N13, 11N32, 11A41, 11N05, 11Y35, 11Y60
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