Question

Let p and p+2 be prime numbers (i.e they are twin primes) with p>3. Show that 6|(p+1) ​

Answer 1

from the well known theorem that, primes are multiple of 6 ±1 ( eg 5,7,11,13,17,19...)

and one of them has $-1$ and other has $+1$ from the multiple of 6

let , $p=6n-1$, so $p+2=6n+1$

$\implies p+1=6n$

$\therefore 6|(p+1)$

QED