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 2005-05-06, 14:07 #1 T.Rex     Feb 2004 France 929 Posts LLT numbers, linkd with Mersenne and Fermat numbers Hi, I've derived from the Lucas-Lehmer 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
 2005-05-06, 16:33 #2 Orgasmic Troll Cranksta Rap Ayatollah     Jul 2003 641 Posts watch out for scathing replies, you're definitely abusing terminology here.
2005-05-06, 19:42   #3
T.Rex

Feb 2004
France

11101000012 Posts

Quote:
 Originally Posted by TravisT watch out for scathing replies, you're definitely abusing terminology here.
Hi TravisT, what's wrong with my paper ? I'm playing with numbers. I did not say I've discovered a magic new method for proving primality of any number. I've just defined and studied the numerical properties of a kind of numbers and noticed some interesting possible properties that need proofs. Can you help me fixing the terminology problems you've noticed ? Can you help providing proofs ?
Thanks,
Tony

2005-05-06, 20:51   #4
Orgasmic Troll
Cranksta Rap Ayatollah

Jul 2003

641 Posts

Quote:
 Originally Posted by T.Rex Hi TravisT, what's wrong with my paper ? I'm playing with numbers. I did not say I've discovered a magic new method for proving primality of any number. I've just defined and studied the numerical properties of a kind of numbers and noticed some interesting possible properties that need proofs. Can you help me fixing the terminology problems you've noticed ? Can you help providing proofs ? Thanks, Tony
taking the "coefficients" of a "function" seems to be a meaningless statement and caught me off guard when I read it. You're taking the coefficients of the polynomials. Since you're never using L as a function, why word it such? In other words, you're never passing a value to L.

I would talk about a set of polynomials Pn where P0 = x and Pn = Pn-12-2 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

 2005-05-07, 08:25 #5 T.Rex     Feb 2004 France 11101000012 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^2-3 has also interesting properties. So, is there a miracle ? or are these properties an evident consequence of some well-known theorem I'm not aware of ? Thanks for your comments ! Tony Last fiddled with by T.Rex on 2005-05-07 at 08:25

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