One day the mathematician G.H. Hardy was visited his collegue Ramanujan:
"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."
<div id="first-passage"> [[1729|133x13]] = ([[1^3|Not Prime]]) + ([[12^3|72x24]]) = [[3|Prime]] + [[1728|96x18]]
[[1729|7x247]] = ([[9^3|243x3]]) + ([[10^3|500x2]]) = [[729|27x27]] + [[1000|125x8]] <div>
<div>
= [[36|6x6]] x [[6x8]][[Is Prime|1729]]= [[6|2x3]] x [[8|2x4]]= [[2x3]]x[[2x3]]= [[2|Prime]] x [[3|Prime]]= [[2|Prime]] x [[4|2x2]][[is both Not Prime and Not Not Prime|1729]]= [[2|Prime]] x [[2|Prime]]= [[9|3x3]] x [[27|9x3]]= [[3|Prime]] x [[3|Prime]]= [[40|8x5]] x [[25|5x5]]= [[8|2x4]] x [[5|Prime]]= [[5|Prime]] x [[5|Prime]]= [[133|7x19]] x [[13|Prime]]= [[7|Prime]] x [[19|Prime]]= [[243|3x27]] x [[3|Prime]]= [[9|3x3]] x [[3|Prime]]= [[9|3x3]] x [[13|Prime]]= [[72|8x9]] x [[24|8x3]]= [[7|Prime]] x [[247|13x19]]= [[500|5x100]] x [[2|Prime]]= [[27|9x3]] x [[27|9x3]]= [[125|5x25]] x [[8|2x4]] = [[96|3x32]] x [[18|6x3]]= [[13|Prime]] x [[19|Prime]]= [[5|Prime]] x [[25|5x5]]= [[3|Prime]] x [[27|9x3]]= [[3|Prime]] x [[32|2x16]]= [[6|2x3]] x [[3|Prime]]= [[2|Prime]] x [[16|2x8]]= [[2|Prime]] x [[8|2x4]]= [[8|2x4]] x [[9|3x3]]= [[8|2x4]] x [[3|Prime]]= [[5|Prime]] x [[100|20x5]]= [[20|2x10]] x [[5|Prime]]= [[2|Prime]] x [[10|2x5]]= [[2|Prime]] x [[5|Prime]]