- #1

kntsy

- 82

- 0

## Homework Statement

prove by induction that the [itex]n^{\text th}[/itex] prime is less than [itex]2^{2^{\text n}}[/itex]

## Homework Equations

hint:assume it is correct for all [itex]n \leq k[/itex], and then compare [itex]p_{k+1}[/itex] with [itex]p_{1}p_{2}...p_{k}+1[/itex]

## The Attempt at a Solution

is [itex]p_{k+1}[/itex] smaller/greater than [itex]p_{1}p_{2}...p_{k}+1[/itex] so that i can extend the use of inequality?

I attempt to use euclidean algorithm but do not know where to use.

Thank you.