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-   -   infinite mersenne prime numbers (https://www.mersenneforum.org/showthread.php?t=26529)

murzyn0 2021-02-22 01:32

infinite mersenne prime numbers
 
2^p - 1, where p is prime number is always prime number, for example:
2^7 - 1 is 127,
2^127 - 1 is 170141183460469231731687303715884105727,
2^170141183460469231731687303715884105727 - 1 is big number, but its prime number, so it's eveidnce that there is infinity mersenne prime numbers

paulunderwood 2021-02-22 01:52

[url]https://primes.utm.edu/mersenne/index.html#unknown[/url]

Proving a ~10^51217599719369681875006054625051616349 digit number prime is beyond all known technolgy.

Batalov 2021-02-22 01:56

[QUOTE=murzyn0;572203]2^p - 1, where p is prime number is always prime number[/QUOTE]
Really?
So if p=11 is a prime number, then 2^11-1 "is always prime number"?

Uncwilly 2021-02-22 01:59

:dnftt:

M344587487 2021-02-22 11:20

Unfortunately you forgot to end with QED so the proof is inadmissible.

murzyn0 2021-02-22 19:48

[QUOTE=Batalov;572206]Really?
So if p=11 is a prime number, then 2^11-1 "is always prime number"?[/QUOTE]

My bad, p must be always result of mersenne prime numbers.

paulunderwood 2021-02-22 21:03

[QUOTE=murzyn0;572271]My bad, p must be always result of mersenne prime numbers.[/QUOTE]

2^13-1== 8191 is prime. 2^8191-1 is not. Easy to check.

murzyn0 2021-02-22 21:33

[QUOTE=paulunderwood;572276]2^13-1== 8191 is prime. 2^8191-1 is not. Easy to check.[/QUOTE]


but, 13 in 2^13-1 is not a mersenne prime numbers.

2^p - 1, where p is a mersenne prime, yields a different mersenne prime.

Viliam Furik 2021-02-22 21:39

[QUOTE=murzyn0;572279]but, 13 in 2^13-1 is not a mersenne prime numbers.

2^p - 1, where p is a mersenne prime, yields a different mersenne prime.[/QUOTE]

But that's not proven. And no, 3 examples are not proof.

Dr Sardonicus 2021-02-22 21:52

[color=red][b]MODERATOR NOTE:[/b] Thread closed.[/color]

retina 2021-02-23 03:19

[QUOTE=murzyn0;572203]2^p - 1, where p is prime number is always prime number, for example:
2^7 - 1 is 127,
2^127 - 1 is 170141183460469231731687303715884105727,
2^170141183460469231731687303715884105727 - 1 is big number, but its prime number, so it's eveidnce that there is infinity mersenne prime numbers[/QUOTE]Eveidnce [sic] != proof.[QUOTE=murzyn0;572279]but, 13 in 2^13-1 is not a mersenne prime numbers.

2^p - 1, where p is a mersenne prime, yields a different mersenne prime.[/QUOTE]2^5-1 (=31) is prime. 2^31-1 is prime. But 2^(2^31-1)-1 is composite, factors are known.

How back to you go? Because 5 is not a Mersenne prime. And your example above, 2 is not a Mersenne prime either, so the sequence 2, 3, 7, 127, ... doesn't start with a Mersenne prime.

And if you conveniently ignore the first term then 3, 7, 127, ... does match your claim, but then 31, 2147483647, ... fails your claim. You can't have it both ways.

:crank:


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