PRIMES OF THE FORM p = 1 + m 2 + n 2 IN SHORT INTERVALS
نویسندگان
چکیده
In this note, we prove that for every θ ≥ 115 121 and x ≥ x0(θ), the short interval (x, x + xθ] contains at least one prime number of the form p = 1+m2 +n2 with (m,n) = 1. This improves a similar result due to Huxley and Iwaniec, which requires θ ≥ 99 100 . §
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Prime numbers of the form p = m 2 + n 2 + 1 in short intervals
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