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Old 2005-05-06, 14:07   #1
T.Rex's Avatar
Feb 2004

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Default LLT numbers, linkd with Mersenne and Fermat numbers

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 P├ępin's tests .

Does someone have hints for proving these properties ?


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