# A question on prime sequence [closed]

Let $\{P_n\}, n\in \mathbb{N}$ be the sequence prime numbers such that $P_1=2, P_2=3\dots$.

Define a new sequence $\{S_n\}$ such that $S_n=P_n+2$ $\forall n\in \mathbb{N}$.

Now the question is: For every prime $p$, does there exist an $N\in \mathbb{N}$, such that $p|S_N$ ?

## closed as off-topic by user26857, Davide Giraudo, Daniel W. Farlow, C. Falcon, NamasteMay 28 '17 at 0:06

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user26857, Davide Giraudo, Daniel W. Farlow, C. Falcon, Namaste
If this question can be reworded to fit the rules in the help center, please edit the question.

The question is whether for all $p$ there is a prime $q$ with $q\equiv -2\pmod p$. When $p$ is odd, this is a special case of Dirichlet's theorem on primes in arithmetic progressions.
• ... and when $p$ is even it's obviously false. – Robert Israel May 25 '17 at 17:12
• @RobertIsrael $q=2$... – Oussama Boussif May 25 '17 at 17:13