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Old 2022-06-11, 09:07   #1
Jinyuan Wang
 
Jan 2020

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Default 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 A354167 and A354168?
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Old 2022-06-11, 09:57   #2
Batalov
 
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"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

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How original!

You are in luck - this has been done multiple times. See the summary here - https://mersenneforum.org/showpost.p...4&postcount=39

Also, see simply A123271. Sign of the penultimate term of the Lucas-Lehmer sequence.
Or Wikipedia: https://en.wikipedia.org/wiki/Lucas%...nultimate_term
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