Show that for every $n \in \Bbb N$ there are at least $\log_2 \log_2 (n+1)$ prime numbers between 1 and $n$.

Asked Mar 10 '16 at 07:41

Active Mar 10 '16 at 07:41

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Question Show that for every $n \in \Bbb N$ there are at least $\log_2 \log_2 (n+1)$ prime numbers between 1 and $n$.

Proof We only studied the prime number limit, and I can't see how to use it here. Also tried induction but I get stuck in the inductive step because I don't know how use the induction hypothesis in this case.

Would like some assistance (first week number theory difficulties...)

asked Mar 10 '16 at 07:41

jreing

3,297

Have you heard about Euclid algorithm ? – openspace Mar 10 '16 at 07:46
yes. How do I use it here? – jreing Mar 10 '16 at 07:50
look for proof of Euclid – openspace Mar 10 '16 at 07:51
I can't even figure how this is related to the problem. From what I figure, maybe between n and n+1 there are more primes, but I don't know how many are there. Also I know that if one of the 2 nums is prime then gcd(a,b)=1. – jreing Mar 10 '16 at 08:24

Show that for every $n \in \Bbb N$ there are at least $\log_2 \log_2 (n+1)$ prime numbers between 1 and $n$.

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