A number which is not divisible by any number except 1 & itself, is called Prime Number.

e.g. 2, 3, 5, 7, 11, 13, 37 etc

The sum of first five prime numbers is:

1. 11

2. 18

3. 26

4. 28

1 is NOT prime number.

So first five prime numbers would be 2, 3, 5, 7, 11

Every prime number will leave +1 or -1 remainder when divided by 6.

i.e. every prime number can be represented in the form of (6n+1) or (6n-1).

Notice the following prime numbers:

5, 7, 11, 17, 19, 23, 29, 31, 37, 41, 43

Each of these numbers can be represented in the form of (6n+1) or (6n-1).

5= 6*1-1

7= 6*1+1

19=6*3+1

23=6*4-1

Vice-versa is not true. That means every number which can be represented in the form of (6n+1) or (6n-1) need not to be prime number necessarily.

e.g. 49 can be represented as 6*8+1 but 49 is not a prime number.

If you are asked to check if a number is prime or not, you will follow the below steps:

1. Check if number can be presented in the form of (6n+1) or (6n-1).

2. If number can’t be presented that means its not a prime number.

3. If number can be presented then it might be a prime number, but you can’t conclude.

In competitive exams, questions are designed in such a way that rejecting the wrong options is more important than getting the right answer in absolute terms. Three wrong options, automatically give you the right answer.

The product of two prime numbers can never be a prime number.

e.g. 2 is a prime number, 7 is also a prime number but 2 X 7 = 14 can never be a prime number.

or 11 is a prime number, 17 is also a prime number but 11 X 17 = 187 can never be a prime number.

And it is quite obvious to understand why product of two prime numbers will never be prime number.

Sum of two prime numbers is NOT necessarily a prime number.

e.g. 3 (prime) + 7 (prime) = 10 (Not prime)

2 (prime) + 3 (prime) = 5 (Prime)

Find the product of all prime numbers between 1 & 20.

1. 9699465

2. 9699690

3. 9699680

4. 9699670

Solution: List out prime numbers upto 20.

2, 3, 5, 7, 11, 13, 17, 19

Desired number = product of 2, 3, 5, 7, 11, 13, 17, 19

Notice that 3 is one of the factor of desired number.

Check quickly, the answer must be divisible by 3. Check if this divisibility test helps you in rejecting all the wrong answers.

By the way upto 20, you can manage by multiplying prime numbers but how will you do if I ask you multiplication of prime numbers upto 100.

Here the small observations like divisibility by 3 or 11 etc may help you in rejecting the wrong answers.

More detailed article and questions on this topic are coming soon.

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