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## Large gaps between sums of two squares

arxiv.org. math. Cornell University, 2019. No. 1906.09100.
Kalmynin A. B., Конягин С. В.
Let S={s1<s2<s3<…} be the sequence of all natural numbers which can be represented as a sum of two squares of integers. For X≥2 we denote by g(X) the largest gap between consecutive elements of S that do not exceed X. We prove that for X→+∞ the lower bound g(X)≥(390/449−o(1))lnX holds.  This estimate is twice the recent estimate by R. Dietmann and C. Elsholtz.