Heegner Number - Almost Integers and Ramanujan's Constant

Almost Integers and Ramanujan's Constant

Ramanujan's constant is the transcendental number, which is an almost integer, in that it is very close to an integer:

262,537,412,640,768,743.999 999 999 999 25…

This number was discovered in 1859 by the mathematician Charles Hermite. In a 1975 April Fool article in Scientific American magazine, "Mathematical Games" columnist Martin Gardner made the (hoax) claim that the number was in fact an integer, and that the Indian mathematical genius Srinivasa Ramanujan had predicted it—hence its name.

This coincidence is explained by complex multiplication and the q-expansion of the j-invariant.