mersenneforum.org Researching k*2^n PLUS 1
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 2007-05-06, 20:30 #1 gd_barnes     May 2007 Kansas; USA 5·13·157 Posts Researching k*2^n PLUS 1 I'm new to this project and the forum. I have 3 questions for the forum: 1. Has much thought been given to researching primes of the form k*2^N+1? 2. Is there a program that currently tests +1. If not, can the LLR program be changed to test +1 vs. -1 -or- is there a 'parameter' or something of the sort that can be put in one of the LLR files that 'causes' it to test +1 instead? 3. Can anyone give me a reason why -1 is better than +1, except that it produces far more primes of the form 2^N-1 (without the k multiplier), which is where this all started. I ask #3 because when applying the k multiplier, it appears that there should be just as much of a chance of +1 being prime as -1, depending on what k you use. For instance, I'm kind of fond of k=105, i.e. 3x5x7. That in conjuntion with either the +1 or -1 guarantees that no candidate of n will have a prime factor of < 11. And in the case of k=105, there are actually more primes with +1 then -1, at least for n < 100. I tested that with my own 'little meager' programs on my own before discovering this project on the web and the amazing programming involved in all of it. The LLR program confirmed that my -1 primes were correct. Because k=105 'appears' to yield more primes from +1 then -1, at least at small values, I would like to do a lot of +1 testing and research on it. I also think there would be many other values of k where +1 should yield more primes than -1. Thanks for any help anyone can give. Gary
 2007-05-06, 23:42 #2 VBCurtis     "Curtis" Feb 2005 Riverside, CA 22×23×47 Posts Hi, welcome to the forums. Check www.prothsearch.net for status of the +1 search. k=105 is tested to 600k according to that site. LLR can test +1 numbers by default-- the top input line has codes that tell LLR whether the list of numbers is -1 (riesel) or +1 (proth) numbers. The srsieve family of programs sets this parameter automatically when you build the sieve, as does NewPGen. You are generally correct that Proths and Riesels are similar in density; RPS just happens to focus on Riesels. -Curtis
 2007-05-09, 03:14 #3 gd_barnes     May 2007 Kansas; USA 5·13·157 Posts Thanks Curtis. I got everything that I needed from the prothsearch site. Gary

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