Happy New Year

We thought of releasing this article on third January because it is the day when Earth is closest to the sun, i.e. Perihelion point, and also because we slept whole day on New Year thanks to late night movie. First we thought of doing an article on the history of calendars and what is the probable reason for February having 28 days and the leap years stuff but there are many videos and blogs which take care of this and explain it in a beautiful way, we’ll post the links of those in the end, so we decided to talk about something else about this year which also has some mathematical significance.

 

Okay, so what is the first thing that comes to mind when you see the number 2017. Prime number of course. Well, if you are a geek like us. Yes, this year is the prime number year, but it is not just any other prime number year, it is the Sexy Prime Number year. Confused? Lets take a look.

 

The largest known prime number as of beginning of 2017 is 2^74,207,281 − 1, a number with 22,338,618 digits. It is a Mersenne prime. Any prime number which can be written in the form 2^n − 1 is called a Mersenne prime. What about 2017? Well, 2017 can be written as 2018-1, but unfortunately 2018 is not a power of 2, so 2017 is not a Mersenne prime. But hey there are hundreds of prime number types. Some interesting types include Pythagorean prime, which is a prime number which can be expressed in the form 4n+1 where n is an integer. 2017 can be expressed in this form as 4×504+1=2017. So yes 2017 is a Pythagorean prime number.

 

One more type of prime number which we found fascinating was Happy primes. In order to understand Happy primes, we need to understand Happy numbers. Consider a number, say 19. Now square and add the individual digits – 1^2 + 9^2 = 82. Continue the process again and again and again, till you get 1.

1^2 + 9^2 = 82

8^2 + 2^2 = 68

6^2 + 8^2 = 100

1^2 + 0^2 + 0^2 = 1

Once you get one, you will see that if you repeat the same process again and again, you will still get one. If the chain ends at 1, that number is called a happy number. And the prime numbers which are happy are called happy primes. So 7, 13, 19, etc. are happy primes.

We tried doing it for 2017. It is not a happy prime, probably because 2016 year was depressing for it too, but something else turned up.

2017

2^2 + 0^2 + 1^2 + 7^2 =54

5^2 + 4^2 = 41

4^2+1^2 = 17

…(continue for a little long)

1^2 + 4^2 + 5^2 = 42

And we get 42, the answer to the life, the universe and everything. The best two digit number, although some argue that it’s 69.

Coming back to the introductory paragraph, we said that 2017 is a sexy prime. Well, sexy refers to the Latin word “sex” meaning “six.” So a pair of prime numbers which differ by 6 are called sexy primes. 2017 and 2011 are both prime numbers and the difference between them is six, so both are sexy prime numbers.

 

My happy new year tweet had a little amount of geekiness, with binary numbers. It was my tweet number 111, which is a repunit number. It is a number containing just the digit 1. And the prime number which is also a repunit (eg. 11) is called the repunit prime.

 

2017 is 306th Prime Number, and we hope this year will be of prime quality.

 

Links you may like

 

https://en.wikipedia.org/wiki/Mersenne_prime

https://en.wikipedia.org/wiki/Largest_known_prime_number

https://en.wikipedia.org/wiki/Sexy_prime

https://en.wikipedia.org/wiki/Repunit

https://en.wikipedia.org/wiki/Happy_number

https://en.wikipedia.org/wiki/Pythagorean_prime

https://simple.wikipedia.org/wiki/Perihelion

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