one hundred sixty-three

Of Martin Gardner’s April Fool’s hoaxes, perhaps the most famous comes from the April 1975 issue of Scientific American, in which he claimed that Srinivasa Ramanujan had proven that eπ163 is exactly equal to an integer. The truth is that it is not, but it comes surprisingly close, being approximately .0000000000007499274028018143 short of the nearest integer.

One hundred sixty-three also appears in an approximation of π, namely,


but this is barely correct to three decimal digits.

There are other qualities of 163 that are somewhat more exact, such as the fact that


Kurt Heegner proved that n=163 is the largest value for which the imaginary quadratic fieldMathworldPlanetmath (-n) has a unique factorization (thus 163 is the largest Heegner number).

Among the real integers, 163 is a prime numberMathworldPlanetmath. As 163+0i, it is also a prime on the complex planeMathworldPlanetmath, that is, a Gaussian primeMathworldPlanetmath.

163 is the eighth prime that is not a Chen primeMathworldPlanetmath. Nor is it a palindromic primeMathworldPlanetmath in any base from binary to base 161 (hence it’s a strictly non-palindromic number).

Title one hundred sixty-three
Canonical name OneHundredSixtythree
Date of creation 2013-03-22 16:54:16
Last modified on 2013-03-22 16:54:16
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 5
Author PrimeFan (13766)
Entry type Feature
Classification msc 11A99
Synonym one hundred and sixty-three