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Question: Mersenne prime guess

Question:Mersenne prime guess

lijinfeng 5 Maple
prime
October 11 2022
1 
After I refer to the Mersenne prime number table, I found the following result
5, 31, the number of digits is too large to be determined
13, 8191
17, 131071
19, 524287
If the following elements all yield composite numbers
So:
2, 3, 7, 127
The length of the sequence with only 2 only generators reaches 4.
Due to its particularity, it is guessed whether 2^(2^127-1)-1 is also a prime number,
and whether the sequence with 2 as the generator is an infinite sequence of prime numbers Woolen cloth? 
Then perfect numbers are also infinite.
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