Co-prime numbers

Set of  numbers that have only common divisor as 1 are called co-prime numbers.

Co-prime numbers are also known as Mutually prime number or Relatively prime numbers.

How to Check weather two numbers are Prime or not?

Consider any two numbers, if no positive integer divide both the numbers except 1 then the two numbers are called Relatively Prime or Co-prime.

Example1: are 15 and 22 co-prime?

Answer: 

Divisors of 15: 1, 3, 5, 15

Divisors of 22: 1,2,11,22

Since 15 and 22 don't have any common divisor they are co-prime.

Example2: are 20 and 34 co-prime?

Answer: 

Divisors of 20 : 1,2,4,5,10,20

Divisors of 34 : 1,2,17,34

These two numbers have 2 as the common divisors so they are not co-prime.

FACTS:

• Every number is co-prime with 1.
• Two even number can never be co-prime because every even number is divisible by 2.
• Every Prime number is co-prime to each other. 
• Any two consecutive number are always co-prime. Take any two number like (1,2), (2,3), (3,4)... (501,502).... are always co-prime.

                                                            

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INAUSPICIOUS NUMBER 13?

        A popular maxim states that the best way to predict the future is to look into the past. History has repeatedly proven the number 13 to be a diabolical entity. sneaking in corners, ready to cause bad omens and accidents, so much so that the fear of this number over the centuries has compounded manifold to the point of causing looks of horrors at the prospect of residing at the "13th floor" of a building.

            The fear of this number has its own personalized jargon known as "Triskaidekaphobia". It is a combination of the Greek words "tris", meaning "three", "kai", meaning "and", "Deka" meaning "ten" and "phobia" meaning "fear".

* Apollo 13 was launched on 11 April and it underwent an explosion on the 13th of April (2 thirteens).

* Zoroastrian tradition predicts chaos in the 13th millennium.

*Another example is the Columbia Space Shuttle. This one went into space on 1/16/2003. Add all the numbers and you will get the number 13. During its re-entry into Earth, it exploded. All the crew members died.

* Many hotels in China and America don't have a 13th floor, After 12th, either they have 12 and a half or 14th. The same goes for the number of houses too.

* Even Microsoft considers the number 13 very unlucky and that is the reason why there is no

version 13 of Microsoft office. Version 12 is Microsoft Office 2007 and the next version Microsoft Office 2010 is actually version 14. Thus, the company skipped the number 13 altogether. 

But just because some superstition is blindly acknowledged, does it make it true? Does this number really deserve this notoriety?

** In ancient Greece, Zeus is considered as the thirteenth and the most powerful God. This thirteenth God seems to be associated with totality, completion, and attainment.

** The ladder to eternity has thirteen steps, on reaching the 13th step, it is assumed that your soul attains spiritual completion.

** 13 is a prime number, which means it cannot be divided by any number other than itself. Hence, Symbolizes qualities of incorruptible nature and purity.

** in one of the most powerful civilizations of history, the Aztecs decided to have 13 days in a week as they considered 13 to him an extremely lucky number. Each day was ruled by one God. And the God who ruled the thirteenth day was associated with mystery, psyche, and magic.

** As we all know 13 is the age of change or transition for every girl or boy. It is the age when children officially become teenagers.

** The US flag has 13 strips, that represent the union of 13 colonies to fight British rule, later these 13 colonies became the first thirteen states of the United States of America.

**The Thai New Year (Songkran Day) is celebrated on the 13th of April. It is considered to be a day of washing away all the bad omens, by splashing water on people, friends, and relatives.

** In Hindu mythology. MahaShivratri is celebrated on the thirteenth night of the Magha month. which is very sacred and a holy night for all the Shiva devotees.

** In the sacred book of the Sikhs, the "Guru Granth Sahib", the word "Waheguru" which means eternal guru appears 13 times.

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Prime Number

A whole number greater than 1 which has only two factors, 1 and the number itself is called Prime number.

Example:- 2,3,5,7,11,13......

FACTS:

• 1 is neither a prime nor a composite number.
• 2 is the only even prime number.
• There are 25 prime numbers between 1 and 100.
• Every Prime number except 2 is an odd number.
• Every number greater than 1 can be divided by at least one prime number.
• Every even positive integer greater than 2 can be expressed as the sum of two primes.
• There are infinite number of Primes.
• Till date the largest known prime number is   (2^82,589,933 − 1) which has 24,862,048 digits.

                                                                                           
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