Landau–Ramanujan constant


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/{sqrt{ln(x).

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_{x ightarrowinfty} frac{N(x)sqrt{ln(x){x}approx 0.76422365358922066299069873125.

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