3 primes conjecture

Question

let be $ p,q,r $ prime numbers AND 'n' an integer

is then true that we can always look for p,q,r and an integer n so

$$ p^{n}+q=r $$

abnd so on

What? Which numbers are supposed to be fixed, and which are to be found?
if you mean infinitely many solutions of the diophantine equation, then it's (1) obviously true (2) no method on earth can prove it. You could restate it: do infinitely many prime powers occur in the difference set $\mathbb P - \mathbb P$. Probably every number occurs. Goldbach asks about $\mathbb P + \mathbb P$.
@user58512 You should usually give some hint why, rather than what appears to be snark. From the nature of the question, the poster is either a beginner (and hence won't get subtle math jokes,) or not a native English speaker (with the same result.)
@ThomasAndrews, why what? by the way I didn't make any jokes - just said what I think about the problem.

Yimin · Answer 1 · 2013-03-01 21:21:31Z

If $n=1$, it is twin prime. Twin prime

If $n\ge 2$. we can see if $p=2$, then the problem is

$2^n+q = r$, actually it is Polignac's conjecture.Polignac

if $q=2$, then the problem is

$p^n+2 = r$, it is something like twin prime.

1 Answer