Blog Post #57 - Prime numbers around 1729

This is a recap of one of my earlier post but with few more details around on prime factorization for one of the most famous number - "RAMANUJAM NUMBER - 1729"

Here are more amazing facts about this number that's not very obvious...

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

1729 in turn is 13 x 7 x 19 (13, 7, 19 are all prime numbers!)

Now look at the odd number anagrams on 1729...

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

Note that odd anagrams are either prime or have factors which are prime and cannot be broken down further

Dig deeper... (Some of these in turn are sum of squares +/- prime number)

1279 is (36 ^ 2) - 17
1296 is (36 ^ 2) + 1
1927 is (44 ^ 2) + 17
9127 is (96 ^ 2) - 89
9217 is (96 ^ 2) + 1

Hats off to the Number 1729 again!