# 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 ${e}^{\pi \sqrt{163}}$ 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 $\pi $, namely,

$$\frac{{2}^{9}}{163}\approx \pi ,$$ |

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

$$\sum _{i=0}^{4}\left(\genfrac{}{}{0pt}{}{8}{i}\right)=163.$$ |

Kurt Heegner proved that $n=163$ is the largest value for which the imaginary quadratic field^{} $\mathbb{Q}(\sqrt{-n})$ has a unique factorization (thus 163 is the largest Heegner number).

Among the real integers, 163 is a prime number^{}. As $163+0i$, it is also a prime on the complex plane^{}, that is, a Gaussian prime^{}.

163 is the eighth prime that is not a Chen prime^{}. Nor is it a palindromic prime^{} 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 |