87539319

 In the television show Futurama, there is a taxicab number 87539319.

 


A famous anecdote of the British mathematician G. H. Hardy regarding a visit to the hospital to see the Indian mathematician Srinivasa Ramanujan. In Hardy's words:

“

I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."

Ever since then, the lowesat number that can be expressed as the sum of 2 positive cubes in n different ways is called a "taxicab number"  1729 is Taxicab(2) because n is 2.


87539319 is Taxicab(3).  It is the lowest number that can be written as the sum of 2 positive cubes in 3 different ways.

Taxicab(3) = 87539319
= 167³ + 436³
= 228³ + 423³
= 255³ + 414³

^{This property was discovered in 1957.}