# Questions tagged [lucas-lehmer-test]

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11 questions
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### Lucas Lehmer Test

I have tried to write a function that test if it is prime using Lucas Lehmer Test ...
0answers
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### Pell-Lucas number

I'm studying about Pell number and Pell-Lucas number whose have Binet formula $P_n=\frac{\alpha^n-\beta^n}{\alpha-\beta}$ and $Q_n=\alpha^n+\beta^n$, where $\alpha=1+\sqrt{2}$ and $\beta=1-\sqrt{2}$, ...
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### What are some basic properties of the quotient $s_n\over M_p$ where $M_p$ is a Mersenne prime?

I've been exploring the Lucas-Lehmer test for a while now. I already know the square of one Mersenne $(2^n-1)^2$ is $(2^{n-1}-1)(2^{n+1}-1)+2^{n-1}$. Today I'm looking to use the properties of the ...
2answers
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### What area's of mathematics are needed to make a basic understanding of the FFT algorithm ?

I know FFT is used in signal processing ( at last check), the Lucas-Lehmer Test and probably many other things. But what is the Fast Fourier Transform and what area's of math will help me understand ...
2answers
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### Are there other ways of doing the Lucas -Lehmer primality test other than this?

The usual ( but simple version) Lucas-Lehmer primality test, as done on Mersenne numbers ( of form $2^n-1$) is as follows: s_0=4\\s_n=(s_{n-1})^2-2 \pmod {2^n-1}\\if\;s_{p-2}\equiv0\pmod{2^n-1}\\2^...
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### What is the easiest non FFT simplification, of this alternate Lucas-Lehmer test ( from a mathematical standpoint)?

We start, with the original Lucas-Lehmer test format: $s_0=4\\ s_i=s_{i-1}^2-2 \pmod {2^p-1}$ We can note, right away, that all terms are even. Dividing out the factor of 2, we get: \$s_0=2\\ s_i=...