Browse Groups

• A Ramanjan Prime Corollary: 2*p_(i-n) p_i for i k where k = primepi(p_k) = primepi(R_n). That is, p_k is the n th Ramanujan Prime, R_n, and the k th prime.
Message 1 of 1 , Oct 31, 2009
View Source
A Ramanjan Prime Corollary:

2*p_(i-n) > p_i

for i > k where k = primepi(p_k) = primepi(R_n). That is, p_k is the n'th Ramanujan Prime, R_n, and the k'th prime.

Proof:
One can rewrite S. Ramanujan's paragraph 2. of "A proof of Bertrand's postulate" to the above. (link: http://www.imsc.res.in/~rao/ramanujan/CamUnivCpapers/Cpaper24/page1.htm )

Example:

From T. D. Noe's table's (links at:
http://www.research.att.com/~njas/sequences/A104272 ,
http://www.research.att.com/~njas/sequences/A000720 )

p_k = 19403, k = 2197, with n=1000, therefore i >= to 2198 and i-n >= 1198. The 2198th prime is 19417, and the 1198th prime is 9719. 2*9719 = 19438 > 19417.

enjoy,

John W. Nicholson
Your message has been successfully submitted and would be delivered to recipients shortly.
• Changes have not been saved
Press OK to abandon changes or Cancel to continue editing
• Your browser is not supported
Kindly note that Groups does not support 7.0 or earlier versions of Internet Explorer. We recommend upgrading to the latest Internet Explorer, Google Chrome, or Firefox. If you are using IE 9 or later, make sure you turn off Compatibility View.