Hi,

I know that the answer is no, yet I dont know how to prove it wrong. Finding a counterexample is not a good solution because it is a past written exam question with no calculators allowed. The first counterexample is about 30000... Is there a, simple preferred, solution to this problem? (This is asked in a CS discrete math exam)

The original problem is from Rosen Discrete Math, and as follows:

Prove or disprove that $p_1p_2 ... p_n+1$ is prime for every integer n, where $p_i$ is the ith smallest prime number.

Thanks in advance.