(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant 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]

3. 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.

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# Homework Help: Another algebra problem about prime and induction

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