Landau–Ramanujan constant

In mathematics and the field of number theory, the Landau–Ramanujan constant is the positive real number b that occurs in a theorem proved by Edmund Landau in 1908, stating that for large ${\displaystyle x}$, the number of positive integers below ${\displaystyle x}$ that are the sum of two square numbers behaves asymptotically as

${\displaystyle {\dfrac {bx}{\sqrt {\log(x)}}}.}$

This constant b was rediscovered in 1913 by Srinivasa Ramanujan, in the first letter he wrote to G.H. Hardy.