Before going to the topic if 1 is prime number or not, let’s talk about first what is prime number. A prime number (or prime) is natural number or an integer greater than one and is not the product of two smaller numbers. A prime number is number which can be divided by one and number itself. Prime numbers are central in number theory due to ‘Fundamental theorem of Arithmetic’s’. 

Important points about prime number-

• The natural numbers which have more than 2 factors which are greater than 1 and or not prime is known as composite number. 

• Prime numbers are central in number theory due to ‘Fundamental theorem of Arithmetic’s’. 

• The number greater than 1 is prime itself or can be factorized as a product of prime numbers which are unique in their own ways.

• Property of being a prime number is called as ‘Primality’. 

• It is a simple and slow method for the checking the Primality of the given number (n) called ‘Trial Division’.

• One is not a prime number, because it specially excluded from the prime definition. Or one is neither a composite number.

• The set of all prime numbers are denoted by P.

Properties of Prime Numbers:

• There are many properties of prime numbers. Few properties of prime are as follow:
• Unique Factorization: It is defined as writing a number as a product of prime number. That written number is known as prime factorization. For example, 34866 = 2 * 32 * 13 * 149.
• There is infinitely number of prime numbers. The sequence which is used to write the infinite number of prime numbers is as follow 2, 3, 5, 7, 11, 13………
• The number which is greater than 1 is always divided by one of the prime number.
• Even positive integers having greater than amount of 2 is always expressed as sum of two prime numbers.

List of Prime Numbers:

• The number of prime numbers which are present in between one to hundred are as follow:
  • 2,3,5,7,11,13,19,23,17,31,37,41,43,47,53,59,61,61,71,73,79,83,89,97 = total number of prime are 25.
• The number of prime numbers which are present in between 101 to 200 are as follow:
  • 101,013,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199 = total number of prime are 21.

Is 1 a Prime Number?

• No, one is not a prime number because; in one we have only one factor.
• According to definition the given number to be prime number should have two factors.

Why 1 is not a Prime Number?

• The answer to the question why 1 is not a prime number is present in definition itself. 
• The number to be prime number we should have two positive factors.
• But in 1we have only one positive factor that is 1itself, which contradict the rules of the prime number.
• So 1 is not a Prime Number. But it is the most important number in mathematics because it is a basic number for forming the other numbers.

How to find the Prime Numbers:

• To know if the given number prime or not, firstly we have to find the factors of the given number.
• To find the factors of the given number we use factorization method which is widely used methods to find the prime numbers.
• Steps used in factorization method are as follow
  • Step 1: find the factor of the given prime number.
  • Step 2: after finding the factors of given prime number check if it has two factors that is one and number itself or not
  • Step 3: if it has the two factors i.e. one and number itself than the given number is prime number.
  • If it has more than two factors than the given number is not a prime number but it is composite number.

Identifying the large Prime Number:

• We can identify the prime numbers in many ways.
• To identify the large prime numbers we have different methods.
• To methods used to identify the large prime numbers are as follow:
  • If the given large number end with 2, 4, 6, 8 or 0 then the given number is not a prime number instead it is an even number which is divided by 2.
  • By adding the numbers of the given large number and then dividing the result by 3. If the number is divisible by 3 than the given large number is not a prime number.
  • If the results of the 1st two method fails than we can take square root method to find if the given large number is prime or not.
  • All prime numbers are listed within the square root value.
  • The given large number is divided by the prime numbers that are listed in square root value.
  • The result which is obtain by dividing the prime numbers is less than square root values than the given large number is not a prime number; otherwise it is a prime number.
  • If the given large number have 0 and 5 at the end of result than it is not a prime number because; it can be easily divisible by 5.
  • Two is the only even number which is a prime number. All other remaining number is odd numbers.
  • Properties of certain numbers can also be used to find if the given number is prime number or not.

Conclusion:

Here, we learnt why 1 is not a prime number, how to find weather the given number is prime or not and also what difference between prime number and composite number is. We have discussed about the properties of the prime number, how to find the prime numbers, how to identify the larger prime number.