Let P is a prime number such that P2 + 7 are also a prime number then

1.	Let P is a prime number such that P2 + 7 are also a prime number then how many such values of P are possible?1. One2. Two3. Four4. Seven
Answer» Correct Answer - Option 1 : One Given: P is a prime number and P² + 7 is also gives a Prime number Concept Used: The numbers having exactly two factors, one and the number itself is called prime numbers Calculation: Let the P² + 7 is equal to x ∴ X should be prime number If P is 2 ∴ X = P² + 7 = (2)² + 7 = 11, where 11 is a prime number If P is 3 ∴ X = P² + 7 = (3)² + 7 = 16, where 16 is even number If P is 5 ∴ X = P² + 7 = (5)² + 7 = 32, where 32 is even number So, all the values of P other than 2 give the values of X as the even number ∴ Only one value of P is possible which gives the X as a prime number Hence, option (1) is correct 2 is the only even prime number, other are the odd prime number P = 2, P2 + 7 = 4 + 7 = 11.

Let P is a prime number such that P2 + 7 are also a prime number then how many such values of P are possible?1. One2. Two3. Four4. Seven

Answer» Correct Answer - Option 1 : One

Given:

P is a prime number and P² + 7 is also gives a Prime number

Concept Used:

The numbers having exactly two factors, one and the number itself is called prime numbers

Calculation:

Let the P² + 7 is equal to x

∴ X should be prime number

If P is 2

∴ X = P² + 7 = (2)² + 7 = 11, where 11 is a prime number

If P is 3

∴ X = P² + 7 = (3)² + 7 = 16, where 16 is even number

If P is 5

∴ X = P² + 7 = (5)² + 7 = 32, where 32 is even number

So, all the values of P other than 2 give the values of X as the even number

∴ Only one value of P is possible which gives the X as a prime number

Hence, option (1) is correct

2 is the only even prime number, other are the odd prime number

P = 2,

P2 + 7 = 4 + 7 = 11.

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