Thread Rating:
• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Iteration exercises: Lucas-Lehmer-test and Schröder-function Gottfried Ultimate Fellow Posts: 757 Threads: 116 Joined: Aug 2007 04/04/2012, 06:17 AM (This post was last modified: 04/04/2012, 06:28 AM by Gottfried.) Since it is a bit quiet currently someone might enjoy an iteration exercise which I've applied to the Lucas-Lehmer-test for the primality of Mersenne-numbers. The Lucas-Lehmer-test *is* just an application of iteration of some simple function, but it is unusual to express this iteration using the concept of the Schröder-function and the Carleman-matrix. After the coefficients of the Schröder-functions have a simple pattern, that functions could be identified with the cosh and arccosh-functions; an identity which was also already known to Schröder himself and was also introduced and is mentioned in Chris Caldwell's nice Prime-pages. Here is my approach which led to a new "Lucal-Lehmer-Constant" L which allows to do the Lucas-Lehmer-test just by the test $\lceil L^{2^p} \rceil = 0 (mod M_p)$ and if the equality holds, then $M_p$ is prime.(Well, for p>7 we need so many digits of L that the test is not practical) Here is the link: lucasLehmerConstant Enjoy - Gottfried Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Possibly Related Threads... Thread Author Replies Views Last Post Is there a function space for tetration? Chenjesu 0 193 06/23/2019, 08:24 PM Last Post: Chenjesu Degamma function Xorter 0 672 10/22/2018, 11:29 AM Last Post: Xorter Iteration exercises: f(x)=x^2 - 0.5 ; Fixpoint-irritation... Gottfried 23 27,668 10/20/2017, 08:32 PM Last Post: Gottfried Should tetration be a multivalued function? marraco 17 14,925 01/14/2016, 04:24 AM Last Post: marraco Introducing new special function : Lambert_t(z,r) tommy1729 2 3,238 01/10/2016, 06:14 PM Last Post: tommy1729 Tommy-Mandelbrot function tommy1729 0 1,778 04/21/2015, 01:02 PM Last Post: tommy1729 The inverse gamma function. tommy1729 3 7,124 05/13/2014, 02:18 PM Last Post: JmsNxn entire function close to sexp ?? tommy1729 8 8,677 04/30/2014, 03:49 PM Last Post: JmsNxn Problem with infinite product of a function: exp(x) = x * f(x)*f(f(x))*... Gottfried 5 6,361 07/17/2013, 09:46 AM Last Post: Gottfried Proof Ackermann function extended to reals cannot be commutative/associative JmsNxn 1 2,835 06/15/2013, 08:02 PM Last Post: MphLee

Users browsing this thread: 1 Guest(s)