## Palindrome and Prime

93639 (a palindromic number) plus the sum of its prime factors is equal to 93683, which is a prime number:

93683 = 93639 + 3 + 7 + 7 + 7 + 7 + 13

Interestingly, there is no prime number between 93639 and 93683.

## And it Continues…

(15 + 25) + (17 + 27) = 2 (1 + 2)4

(15 + 25 + 35) + (17 + 27 + 37) = 2 (1 + 2 + 3)4

(15 + 25 + 35 + 45) + (17 + 27 + 37 + 47) = 2 (1 + 2 + 3 + 4)4

(15 + 25 + 35 + 45 + 55) + (17 + 27 + 37 + 47 + 57) = 2 (1 + 2 + 3 + 4 + 5)4

etc.

## Power Relationships

6205 = 38² + 69² and 3869 = 62² + 05²

5965 = 77² + 06² and 7706 = 59² + 65²

The following is less obvious and it involves cubes instead of squares:

244 = 1³ + 3³ + 6³ and 136 = 2³ + 4³ + 4³

My name Edmark M. Law. I work as a freelance writer, mainly writing about science and mathematics. I am an ardent hobbyist. I like to read, solve puzzles, play chess, make origami and play basketball. In addition, I dabble in magic, particularly card magic and other sleight-of-hand type magic. I live in Hong Kong. I blog at learnfunfacts.com. You can find me on Twitter @EdmarkMLaw and Facebook. My email is learnfunfacts@gmail.com
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### 5 Responses to Curious Number Patterns #3

1. Nice!! I love math!!

Liked by 1 person

2. Jack Shalom says:

Nice. I don’t know if you’ve done a post on amicable numbers yet:
https://en.wikipedia.org/wiki/Amicable_numbers

Liked by 1 person