Prime Range

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Rabeeb
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Location:Mymensingh, Bangladesh
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Prime Range

Unread post by Rabeeb » Sat Sep 14, 2013 11:51 pm

Prove that any prime number is less than thrice the previous prime number

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Fm Jakaria
Posts:79
Joined:Thu Feb 28, 2013 11:49 pm

Re: Prime Range

Unread post by Fm Jakaria » Mon Sep 16, 2013 12:58 am

In fact, Bertrand's postulate states that:
For any positive integer n > 1, there is a prime number strictly between n and 2n.
Now denote the k'th prime by p(k). We set n = p(k - 1) for k > 1 a positive integer. So p(k-1) < P(k) < 2p(k-1) < 3p(k-1); which establishes the fact to be achieved.
You cannot say if I fail to recite-
the umpteenth digit of PI,
Whether I'll live - or
whether I may, drown in tub and die.

Rabeeb
Posts:25
Joined:Tue Dec 14, 2010 7:52 pm
Location:Mymensingh, Bangladesh
Contact:

Re: Prime Range

Unread post by Rabeeb » Thu Sep 19, 2013 3:17 pm

:D Well, u got a simpler proof... Didn't know about Bertrand's Postulate earlier... I was thinking to work out with Goldbach's Weak Conjecture instead...

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