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Abstract
Let $N$ be a sufficiently large integer. It is proved that the inequality $ \left| N - p^2 - q^2 \right| < H $ is solvable in primes $p, q$ providing $H > N^{\frac{151}{320} + \varepsilon}$. This improves previous results of Naumenko.
Sums of two squares of primes in short intervals
18 December 2025, Version 1
Working Paper
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Dec 18, 2025 Version 1
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