Question

If p, p+2, p+4 are prime numbers, then the number of possible solutions for p is?

Answer 1

There is only one solution for p.

Step-by-step explanation:

Let us see the list of prime numbers:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, ... ...

Given, 3rd prime number = p + 4, 2nd prime number = p + 2 and first prime number = p.

Here, (p + 4) - (p + 2) = (p + 2) - p = 2; that is the difference between consecutive prime numbers is 2.

This is only possible when the prime numbers are 3, 5 and 7.

• 7 - 5 = 2
• 5 - 3 = 2

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