Question

A prime number $p$ is called special if there exist primes $p_1,p_2,p_3,p_4$ such that $p=p_1+p_2=p_3-p_{4.}$ The number of special primes is

• A. 0
• B. 1
• C. more than one but finite
• D. infinite

Answer 1

Answer: (B)

It is given that for prime numbers $p_1,p_2,p_3,p_4$ the special prime
number

$p=p_1+p_2=p_3-p_4$

Case I

If all $p_1,p_2,p_3,p_4$ are odd, then $(p_1+p_2)$

and $(P_3-P_4)$ are even, which is not possible

Case II
If one of $p_1$ and $p_2$ is even, say $p_2$ is 2 and $p_4$ must be 2.

So, $p=p_1+2=p_3-2$

the above equation is satisfied only if

$p=5,p_{1}3$ and $p_3=7$

So, the number of special prime p is $1$