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Landau–Ramanujan constant

In mathematics, the Landau–Ramanujan constant occurs in a number theory result that the proportion of positive integers less than x which are the sum of two square numbers is, for large x, varies as

$x/\left\{sqrt\left\{ln\left(x\right)\right\}\right\}.$

The constant of proportionality is the Landau–Ramanujan constant, which was discovered independently by Edmund Landau and Srinivasa Ramanujan.

More formally, if N(x) is the number of positive integers less than x which are the sum of two squares, then

$lim_\left\{xrightarrowinfty\right\} frac\left\{N\left(x\right)sqrt\left\{ln\left(x\right)\right\}\right\}\left\{x\right\}approx 0.76422365358922066299069873125.$