Geodesic
Approaching real numbers by sums of squares of two primes
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2019), pp. 51-55

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It is proved that a given real number $N>N_0(\varepsilon)$ can be approached by the sum of squares of two primes to the distance not exceeding $H = N^{31/64-1/300 + \varepsilon}$, where $\varepsilon$ is an arbitrary positive number. 
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     author = {A. P. Naumenko},
     title = {Approaching real numbers by sums of squares of two primes},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
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A. P. Naumenko. Approaching real numbers by sums of squares of two primes. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2019), pp. 51-55. http://geodesic.mathdoc.fr/item/VMUMM_2019_5_a9/