20220611, 09:07  #1 
Jan 2020
5_{8} Posts 
Categorize Mersenne Primes with LL test

20220611, 09:57  #2 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9989_{10} 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 LucasLehmer sequence. Or Wikipedia: https://en.wikipedia.org/wiki/Lucas%...nultimate_term 
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