Blog Post # 85 - Interesting pattern of prefixes

Take 729 which is a perfect square (27 x 27)

Now prefix 1 - 1729 which is Ramanujam number and also 19 x 91 (19 and 91 are anagrams)
Now prefix 11 - 11729 which is 37 x 317 (317 has 37 as its subset)
Now prefix 111 - 111729 which is 3 x 37243 (Notice 37 again and 243 x 3 is 729 which is the original number!)
Now prefix 1111 - 1111729 which is 1019 x 1091 - Voila! 19 x 91 component is back again
Now prefix 11111 - 11111729 which is 37 x 300317! (37 and 317 are back!)
Now prefix 111111 - 111111729 which is 3 x 37037243!

To summarize

729 - 27 x 27
1729 - 19 x 91
11729 - 37 x 317
111729 - 3 x 37243
1111729 - 1019 x 1091
11111729 - 37 x 300317
111111729 - 3 x 37037243