Iteration exercises: Lucas-Lehmer-test and Schröder-function - Printable Version +- Tetration Forum ( https://math.eretrandre.org/tetrationforum)+-- Forum: Tetration and Related Topics ( https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1)+--- Forum: Mathematical and General Discussion ( https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3)+--- Thread: Iteration exercises: Lucas-Lehmer-test and Schröder-function ( /showthread.php?tid=730) |

Iteration exercises: Lucas-Lehmer-test and Schröder-function - Gottfried - 04/04/2012
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 and if the equality holds, then 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 |