20050506, 14:07  #1 
Feb 2004
France
3A5_{16} Posts 
LLT numbers, linkd with Mersenne and Fermat numbers
Hi,
I've derived from the LucasLehmer Test a new (??) kind of numbers, that I called LLT numbers. They are described in this short (2.5 pages) paper: LLT numbers . These numbers show interesting numerical relationships with Mersenne and Fermat prime numbers, without any proof yet. First, I'm surprised it is so easy to create such a kind of numbers that have so close relationships with Mersenne and Fermat numbers. Is there a law saying that playing with prime (Fermat and Mersenne) numbers always lead to nice properties ? Second, these numbers may provide interesting primality tests for Fermat and Mersenne numbers (once the properties are proven ...); though they clearly do not improve existing LLT and Pépin's tests . Does someone have hints for proving these properties ? Regards, Tony 
20050506, 16:33  #2 
Cranksta Rap Ayatollah
Jul 2003
1010000001_{2} Posts 
watch out for scathing replies, you're definitely abusing terminology here.

20050506, 19:42  #3  
Feb 2004
France
3·311 Posts 
Quote:
Thanks, Tony 

20050506, 20:51  #4  
Cranksta Rap Ayatollah
Jul 2003
641 Posts 
Quote:
I would talk about a set of polynomials P_{n} where P_{0} = x and P_{n} = P_{n1}^{2}2 where n > 0, I'm no expert, so I may be abusing notation as well. I haven't had time to look at more than a few of the conjectures you've posed, the first few seem like they can be proven (or disproven) without too much effort 

20050507, 08:25  #5 
Feb 2004
France
933_{10} Posts 
Function vs Polynomial
You are perfectly right: I should use polynomial rather than function !
I've fixed the mistakes and produced a new version . Seems polynomial x^23 has also interesting properties. So, is there a miracle ? or are these properties an evident consequence of some wellknown theorem I'm not aware of ? Thanks for your comments ! Tony Last fiddled with by T.Rex on 20050507 at 08:25 
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