13 is not seen as a lucky number by many and there are numerous reasons, examples quoted for the same. But 13 as a number along with its anagram pair 31 displays some incredible patterns and attributes
Here's why I think this number is special
a) 13 squared is 169 and it is one of the first set of Pythagoras family member - 13 ^ 2 = 12 ^ 2 + 5 ^ 2
b) Reverse of 169 is 961 which is 31 ^ 2 and 31 is reverse or anagram of 13
So far so good and most of you must be saying that there's nothing new. Now things get a bit interesting
c) 13 and 31 together is 1331 which is 11 * 11 * 11 and notice the first and last digit and two digits in the middle - 11 and 33 = 11 * 3 = 33 while the number itself is 11 ^ 3! And ofcourse to top it all 1331 is a palindrome!
d) Concatenate 169 and 961 and we get 169961...Without a doubt this a perfect palindrome!! There are only few squares like these which are perfect palindromes - 144 and 441 being the other (12 ^ 2 and 21 ^ 2)
e) Now 169961 is a product of two prime numbers - 11 and 15451... And if we notice 15451 is also a perfect palindrome and a prime number!
f) 13 ^ 3 is 2197 and 31 ^ 3 is 29791 and as we could notice 2197 is a subset of 29791!
Can you find more patterns of this nature? I bet there are few more if we continue to deep dive!
Here's why I think this number is special
a) 13 squared is 169 and it is one of the first set of Pythagoras family member - 13 ^ 2 = 12 ^ 2 + 5 ^ 2
b) Reverse of 169 is 961 which is 31 ^ 2 and 31 is reverse or anagram of 13
So far so good and most of you must be saying that there's nothing new. Now things get a bit interesting
c) 13 and 31 together is 1331 which is 11 * 11 * 11 and notice the first and last digit and two digits in the middle - 11 and 33 = 11 * 3 = 33 while the number itself is 11 ^ 3! And ofcourse to top it all 1331 is a palindrome!
d) Concatenate 169 and 961 and we get 169961...Without a doubt this a perfect palindrome!! There are only few squares like these which are perfect palindromes - 144 and 441 being the other (12 ^ 2 and 21 ^ 2)
e) Now 169961 is a product of two prime numbers - 11 and 15451... And if we notice 15451 is also a perfect palindrome and a prime number!
f) 13 ^ 3 is 2197 and 31 ^ 3 is 29791 and as we could notice 2197 is a subset of 29791!
Can you find more patterns of this nature? I bet there are few more if we continue to deep dive!
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