Question

If a, a + 2 and a + 4 are prime numbers, then the number of possible solutions for a is:

• A. One
• B. Two
• C. Three
• D. Four

Answer 1

The correct option is A One

$a(a+2),(a+4)$ are prime numbers

$\Rightarrow$ difference between (consecutive) these no is $2$-

Prime no are $2,3,5,7,11,.....$

$\therefore$ put $a=3$ yields a set of prime numbers $3,5,7$ having a consecutive difference of ${}^{\prime }{2}^{\prime }$-

& this is only one solution.