Prime Range
Prove that any prime number is less than thrice the previous prime number
- Fm Jakaria
- Posts:79
- Joined:Thu Feb 28, 2013 11:49 pm
Re: Prime Range
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.
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.
the umpteenth digit of PI,
Whether I'll live - or
whether I may, drown in tub and die.
Re: Prime Range
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...