Puzzle No. 52 - Amazing facts of 1729

We all know that 1729 is the ever famous Ramanujam number and even in the past, we have looked at some interesting patterns that emerge out of this number

Here are few more amazing facts about this number that's not very obvious... Focus on the odd number anagrams of 1729 in particular

1729 is 10 ^ 3 + 9 ^ 3 = 12 ^ 3 + 1 ^ 3 (This is the Ramanujam number as we all know)

Now look at the odd number anagrams...

1279 - Prime number
1297 - Prime number
1927 - 41 * 47 - Both are prime in turn
7129 - Prime number
7219 - Prime number
7291 - 23 * 317 - Both are prime in turn
7921 - 89 * 89 which in turn is a prime
9127 - Prime number
9217 - 13 * 709 - Both are prime in turn
9271 - 73 * 127 - Both are prime in turn
9721 - Prime number

It is beautiful to see that all the odd anagrams are either prime or have factors which are prime and cannot be broken down further

This number continues to amaze me everytime I think about the combinations and permutations!