$t_title is "1729"
$t_adjust_path is "/~caldwell/curios/"
$t_class is "composite"
$short is "1729"
$nunber_id is "94"
$t_meta['description'] is "One of many pages of prime number
curiosities and trivia. This page discusses 1729
Come explore a new prime today!"
The Hardy-Ramanujan number is the smallest product of three distinct primes of the form 6n + 1. [Pol]
The largest number which is divisible by its prime sum of digits (19) and reversal (91)
happens to be Ramanujan's famous taxi-cab number
(1729 = 123 + 13 = 103 + 93).
It is the smallest number expressible as the sum of two positive cubes in two different ways.
The smallest number that is a pseudoprime simultaneously to bases 2, 3 and 5. [Pomerance ,
If you reverse the middle digits of this pseudoprime you get 1279 and 21279 - 1 is a Mersenne prime. [Luhn]
Schiemann's first pair of isospectral lattices L+(1,7,13,19) and L-(1,7,13,19) are of determinant 1*7*13*19 = 1729. [Poo Sung]
The Hardy-Ramanujan number is equal to the average of the only known prime squares of the form n! + 1, i.e., 25, 121, and 5041. [Gudipati]
(There are 10 curios for this number that have not yet been approved by an editor.)
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