LLT numbers, linkd with Mersenne and Fermat numbers

[T.Rex]

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

[Orgasmic Troll]

watch out for scathing replies, you're definitely abusing terminology here.

[T.Rex]

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

[Orgasmic Troll]

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 P_n where P₀ = x and P_n = P_n-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

[T.Rex]

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