- #1

cwatki14

- 57

- 0

Let 2 = p1 < p2 < p3... be the sequence of primes in increasing

order. Prove that pn ≤ 2

^{2n-1}.(Hint: Show that the method used to prove Euclid’s Theorem also proves that pn ≤ p1p2...pn−1 + 1.)

So I started doing the proof via induction, letting n=2 be my base case. That's pretty straightforward. I assume that it is true for all n≤k, now I am trying to prove true for k+1.

My issue lies in the fact I don't know how to tie into the method from Euclid's Thm (pn ≤ p1p2...pn−1 + 1) into what I am actually trying to prove (pn ≤ 2

^{2n-1}). Any ideas?