# Pi[x] >=loglogx

by AlbertEinstein
Tags: >loglogx
 P: 113 I am going through Hardy's book on number theory.The following theorem I do not understand. theorem 10: pi[x] >= loglog x where pi[x] is the prime counting function and >= stands for greater than or equal to The arguments written in the book are very compact.please help .
 Sci Advisor HW Helper P: 1,994 Do you follow any of it? Do you understand how they derived $$p_{n}<2^{2^n}$$ ? this is an important step. The rest just follows from pi(x) being increasing, and also $$\pi(p_n)=n$$ which they use but don't explicitly mention.
 Sci Advisor HW Helper P: 3,684 Bertrand's postulate?
 Sci Advisor HW Helper P: 1,994 Pi[x] >=loglogx Nope! the bound of p_n above is much weaker than Bertrand's will give you. It's correspondingly simpler to prove though, it follows from a slight adaptation of Euclid's proof there are infinitely many primes (in case anyone who hasn't seen it wants to give it a stab)