# On the primality of 2^p+3^q

1. Sep 15, 2009

### rrronny

Let $$\mathbb{P}$$ the set of primes. Lets $$p,q \in \mathbb{P}$$ and $$p \le q.$$ Find the pairs $$(p,q)$$ such that $$2^p+3^q$$ and $$2^q+3^p$$ are simultaneously primes.

2. Sep 15, 2009

### Staff: Mentor

You have to show your attempts to receive help. This is a forum policy.

3. Sep 15, 2009

### rrronny

Hi Borek,
I do not have a solution for this problem...
I found only four solutions: $$(1,1), (1,2), (2,3), (2,6).$$

4. Sep 19, 2009

### quantumdoodle

wait... 6 is not a prime...

5. Sep 19, 2009

### ramsey2879

Neither is 1 so only one of the 4 pairs posted is acceptable. There is still another very obvious pair that was overlooked.

6. Sep 19, 2009

### rrronny

Sorry... I meant the sixth prime number.
In summary, then, the only solutions $$(p,q)$$ that I found are $$(2,2),(2,3),(3,5), (3,13).$$