The legend of the taxi-cab number and unknown facts about it.

Harshad Number:

Ivan Niven; Dr. Kaprekar

Carmichael number:

Here, again we are exposed to Fermat’s Little theorem, wonderful how Fermat pops up almost everywhere! Let’s have a look at a test that is applied to check if a number is prime or not and we are going to use Fermat’s little theorem. It says if you have a number, ‘a,’ and you raise it to the power of a number, ‘n,’ and you subtract the original number, ‘a,’ again and this resultant is divisible by n, p has to be be a prime! The mathematical expression for it is:

Euler Pseudoprime:

An odd composite integer n is called an Euler pseudoprime to base a, if a and n are co-prime, and

Sphenic Number:

A sphenic number is any number that can be expressed as the product of three prime numbers. 1729, too is a sphenic number, as 1729 can be expressed as the product of 7, 13, and 19, all of which are primes!

Zeisel number:

Zeisel number, probably first introduced by Kevin Brown, while he was looking for numbers that when plugged into 2^{k-1}+k yielded prime numbers. Later 1885 was pointed out to be such a number by Helmut Zeisel. Soon it was discovered that 1885 has prime factors that follow:

Loeschian number:

Numbers that can be expressed in the form x^2 + x.y + y^2 for integer x, y are called the Loeschian numbers. 1729 is the smallest number that can be expressed as the loeschian number in four different ways, where (x,y) can be: (25,23), (32,15), (37,8) and (40,3).

Galactic Algorithm:

Named after Richard Lipton and Ken Regan, a galactic algorithm outperforms all algorithms for sufficiently large (VERY large) problems. Galactic algorithms have never used for terrestrial data as it is suitable for very large ones.



Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store


Hello there! I am Ahitagni and I love math, physics & cheese!