Question

Every prime number p is always expressible in the form 6k + 1 or 6k + 5 where k ∈ N. (True / False)


Explanation please !!​

Answer 1

Answer:

I know this answer the answer is true

Answer 2

Given :  Every prime number p is always expressible in the form 6k + 1 or 6k + 5 where k ∈ N

To find :  True or False

Solution:

Every prime number p is always expressible in the form 6k + 1 or 6k + 5 where k ∈ N.

This is FALSE

2 is a prime number  can not be expressed as   6k + 1 or   6k + 5

3 is  is a prime number  can not be expressed as   6k + 1 or 6k + 5

After that we can say that  Every prime number p is always expressible in the form 6k + 1 or 6k + 5

as any number can be expressed in form of

6k , 6k+ 1 , 6k + 2 , 6 k + 3 , 6k + 4 , 6k + 5

6k = 2 * 3 k ( not a prime number)

6k + 2 = 2(3k + 1) ( not a prime number)

6 k + 3  = 3(2k + 1)  ( not a prime number)

6k + 4 = 2(3k + 2)   ( not a prime number)

Hence only possible prime numbers are  6k+ 1   , 6k + 5

Hence Every prime number p is always expressible in the form 6k + 1 or 6k + 5 where k ∈ N  for  

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