Categorize Mersenne Primes with LL test

Jinyuan Wang · 2022-06-11, 09:07

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?

Batalov · 2022-06-11, 09:57

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

2022-06-11, 09:07	#1
Jinyuan Wang Jan 2020 5 Posts	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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2022-06-11, 09:57	#2
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2²·5·503 Posts	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