Are two primes always relatively prime? I'm having trouble proving this with contradiction.

First I assume that two primes, p and q are not relatively prime. Therefore there is an x > 1 that divides both p and q.

x | p ... so p = xk

x | q ... so q = xd

Am I on the right track? I think what I need to do is show that x = 1 but I'm not sure how to get there

if p and q are prime numbers, p is dividable only by 1 and p, and q is dividable only by 1 and q. so the only thing that can divide both is 1, unless p=q to begin with not sure it needs a better proff than this, its quite logical to me

yeah it makes sense logically to me I just can't seem to find a way to prove it rigorously

but this kinda proves it, for example take numbers 4 and 22, 4=2*2 and 22=2*11, so the common is 2

with p and q you just have 1*p and 1*q and thats where it ends i mean i like mathematical proving, but this is just so fucking obvious i think this should do

seems you have been given a problem, can be you please state it exactly as it is given to you

True/False? Any pair of primes is relatively prime.

truuuue, unless they are identical numbers!

the answer is true, as you probably know
what is the definition of a,b being co-prime (ie relatively prime)? gcd(a,b)=1
and what is the definition of a prime p? gcd(p,n)=1 for all n=/=p

okay thank you