The Ramanujan constant is an extremely close almost-integer, equal to \(e^{\pi\sqrt{163}} \approx 262537412640768743.9999999999992500725971981\).[1] It came from an April fool's prank by Martin Gardner, where he claimed that \(e^{\pi\sqrt{163}}\) was actually an integer and that Ramanujan himself hypothesized this. Ramanujan had no actual involvement with the number.

The number is not at all a coincidence; \(-163\) is a Heegner number and \(e^\pi\) has important properties on the complex plane.

The prime factorization of 262537412640768744 is 23 × 3 × 10939058860032031.

Sources Edit

  1. Ramanujan Constant

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