# Thread: A problem on primes

1. ## A problem on primes

Hi
I am unable to crack it anyone plz through some light.
if p is a prime,p^2+2 is a prime prove that p^3 +2 is a prime.

2. ## Re: A problem on primes

Originally Posted by Learner248
Hi
I am unable to crack it anyone plz through some light.
if p is a prime,p^2+2 is a prime prove that p^3 +2 is a prime.
Hint:

Any prime number bigger than 3 is congruent to 1 or 5 modulo 6.

3. ## Re: A problem on primes

Originally Posted by Learner248
Hi
I am unable to crack it anyone plz through some light.
if p is a prime,p^2+2 is a prime prove that p^3 +2 is a prime.
If p is prime p=6k+1 or p=6k+5;
1)p=6k+1 then $\displaystyle 3|p^2+2>3$ contradiction
2)p=6k+5,3|$\displaystyle p^2+2>3$ so you have a problem with your problem

4. ## Re: A problem on primes

Originally Posted by TheodorMunteanu
If p is prime p=6k+1 or p=6k+5;
1)p=6k+1 then $\displaystyle 3|p^2+2>3$ contradiction
2)p=6k+5,3|$\displaystyle p^2+2>3$ so you have a problem with your problem

Only p=3 satisfying the problem conditions.