# 3 primes conjecture

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

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

• $5+2=7$
• $2^{3}+3=11$
• $3^{4}+2=83$

abnd so on

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What? Which numbers are supposed to be fixed, and which are to be found? – Chris Eagle Mar 1 '13 at 21:02
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 Mar 1 '13 at 21:04
I think he means for each $n$, we can find $p,q,r$. – Yimin Mar 1 '13 at 21:08
@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.) – Thomas Andrews Mar 1 '13 at 21:08
@ThomasAndrews, why what? by the way I didn't make any jokes - just said what I think about the problem. – user58512 Mar 1 '13 at 21:10

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.