# Math Help - prove,,,

1. ## prove,,,

for $n \in \mathbb{N}$ Let $\ p_n$ \ be the $n^{th}$ prime $(thus \ , p_1=2,p_2=3,p_3=5,p_4=7,p_5=11,...):$
prove that $\ p_n \leq p_1 p_2 p_3...p_{n-1} +1 , n \geq 3$

2. Suppose the next prime wasn't less or equal to your number (A= product of primes + 1). Is A prime? Clearly none of the primes less than A divide it (they all leave a remainder of 1). You have a contradiction.