During one of our conversations one of my pretty close school mate, Ram, said that his favourite number is 1312 and wanted to check if there are any cool attributes associated with this number
Here are few to start with
a) 1312 is sum of two perfect squares - 1296 + 16
b) 13 + 12 and 13-12 are perfect squares again
c) 1312 can be written as 1000 + 156 + 156 which is 10 ^ 3 + 13 x 12 + 13 x 12 - not many numbers exhibit this property where it is a sum of perfect cube (1000) added with a number (156) whose factors (13, 12 here) are sub-digits of the result! (1312)
d) Now this gets interesting - Look at the odd anagrams of 1312
1123 - Prime
1213 - Prime
1321 - Prime
2113 - Prime
2131 - Prime
2311 - Prime
3121 - Prime
3211 - Only exception but the factors are 13 and 19 which are prime numbers again and 13 is the first two digits of 1312!
e) 2131 is the mirror image of 1312 - 21 x 31 = 651 which is the mirror image of 156 (13 x 12)
Ram - over to you to jot down few more :)
Here are few to start with
a) 1312 is sum of two perfect squares - 1296 + 16
b) 13 + 12 and 13-12 are perfect squares again
c) 1312 can be written as 1000 + 156 + 156 which is 10 ^ 3 + 13 x 12 + 13 x 12 - not many numbers exhibit this property where it is a sum of perfect cube (1000) added with a number (156) whose factors (13, 12 here) are sub-digits of the result! (1312)
d) Now this gets interesting - Look at the odd anagrams of 1312
1123 - Prime
1213 - Prime
1321 - Prime
2113 - Prime
2131 - Prime
2311 - Prime
3121 - Prime
3211 - Only exception but the factors are 13 and 19 which are prime numbers again and 13 is the first two digits of 1312!
e) 2131 is the mirror image of 1312 - 21 x 31 = 651 which is the mirror image of 156 (13 x 12)
Ram - over to you to jot down few more :)
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