Question

Find the no of prime number p for which p+2 and p+5 is also a prime?
I found the answer to be 3 which i am not able to understand
for example If we substitute 3 in and p+2 and p+3 ,I am getting 5,8 respectively .8 is not a prime number .

Answer 1

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As the prime numbers are: 2,3,5,7,11,13,17,19,23,29....

Plug in a prime number for p, and see which of the answers is also prime.

Plug p=2 for option A, Then

$\huge \tt \frac{3}{p} = \frac{3}{2}$

,which is not a prime, plugging any prime for p in option A will not give a prime, as prime numbers are only divisible by itself or 1.

Option B,C and E will always give an even value which is divisible by 2, so that can not be a prime as prime numbers are only divisible by itself or 1.

The only answer remaining is D it must be correct, it could be a prime number.

For example p=3 ; p+2=3+2=5 is a prime number.

Answer 2

Answer:

As the prime numbers are: 2,3,5,7,11,13,17,19,23,29....

Plug in a prime number for p, and see which of the answers is also prime.

Plug p=2 for option A, Then

,which is not a prime, plugging any prime for p in option A will not give a prime, as prime numbers are only divisible by itself or 1.

Option B,C and E will always give an even value which is divisible by 2, so that can not be a prime as prime numbers are only divisible by itself or 1.

The only answer remaining is D it must be correct, it could be a prime number.

For example p=3 ; p+2=3+2=5 is a prime number.