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-   -   Categorize Mersenne Primes with LL test (https://www.mersenneforum.org/showthread.php?t=27852)

Jinyuan Wang 2022-06-11 09:07

Categorize Mersenne Primes with LL test
 
We know that M_p is a prime iff b_{p-1} == 0 mod M_p, where b_1 = 4; b_k = b_{k-1}^2 - 2 (mod M_p) for k >= 2.

Then how about b_{p-2} mod M_p? Are there any guys interested in extending OEIS sequence [URL="https://oeis.org/A354167"]A354167[/URL] and [URL="https://oeis.org/A354168"]A354168[/URL]? :banana:

Batalov 2022-06-11 09:57

How original! :rolleyes:

You are in luck - this has been done multiple times. See the summary here - [url]https://mersenneforum.org/showpost.php?p=502204&postcount=39[/url]

Also, see simply A[OEIS]123271[/OEIS]. Sign of the penultimate term of the Lucas-Lehmer sequence.
Or Wikipedia: [url]https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test#Sign_of_penultimate_term[/url]


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