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Mathematics of Computation

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Counting sums of two squares: the Meissel-Lehmer method

Author: P. Shiu
Journal: Math. Comp. 47 (1986), 351-360
MSC: Primary 11Y35; Secondary 11N37, 11P05
MathSciNet review: 842141
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Abstract: In 1870, E. D. F. Meissel developed a method for computing the individual values of the prime-counting function, and, in 1959, D. H. Lehmer simplified and extended Meissel's method. Let $ W(x)$ count the numbers not exceeding x that are sums of two squares. We develop a variant of the Meissel-Lehmer method for $ W(x)$ and use it to calculate $ W({10^{12}})$.

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Keywords: Meissel-Lehmer method, sums of two squares
Article copyright: © Copyright 1986 American Mathematical Society