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 
[url]https://primes.utm.edu/mersenne/index.html#unknown[/url]
Proving a ~10^51217599719369681875006054625051616349 digit number prime is beyond all known technolgy. 
[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 2^111 "is always prime number"? 
:dnftt:

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

[QUOTE=Batalov;572206]Really?
So if p=11 is a prime number, then 2^111 "is always prime number"?[/QUOTE] My bad, p must be always result of mersenne prime numbers. 
[QUOTE=murzyn0;572271]My bad, p must be always result of mersenne prime numbers.[/QUOTE]
2^131== 8191 is prime. 2^81911 is not. Easy to check. 
[QUOTE=paulunderwood;572276]2^131== 8191 is prime. 2^81911 is not. Easy to check.[/QUOTE]
but, 13 in 2^131 is not a mersenne prime numbers. 2^p  1, where p is a mersenne prime, yields a different mersenne prime. 
[QUOTE=murzyn0;572279]but, 13 in 2^131 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. 
[color=red][b]MODERATOR NOTE:[/b] Thread closed.[/color]

[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 2^131 is not a mersenne prime numbers. 2^p  1, where p is a mersenne prime, yields a different mersenne prime.[/QUOTE]2^51 (=31) is prime. 2^311 is prime. But 2^(2^311)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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