Question

If the product of two twin prime numbers and the absolute difference of smallest composite number and the smallest prime number is $646$, then larger prime number is

Answer 1

Smallest composite number is $4$
Smallest prime number is $2$
So, $x(x+2)(4-2)=646$
$\Rightarrow x(x+2)=323$
$\Rightarrow x^2+2x-323=0$
$\Rightarrow x^2+19x-17x-323=0$
$\Rightarrow (x+19)(x-17)=0$
Since, $x=-19$ (not possible)
$\therefore x=17$

Hence, larger prime number is $x+2=19$