2^primenumber -1 is always a prime number ?
 

Hi All,

Please let me know was if 2^8191 -1 proved to be not prime number ?
Since I saw the symmetry till the number ( 2^127-1 ) that 2 power of any primenumber is a primenumber too.


Regards,
Mastan

2^8191 -1 has factors 338193759479, 210206826754181103207028761697008013415622289, so it cannot be prime. End of proof.

Ok, Thanks what about this .


2 ^ 2 ^127 -1 which is more clearly POWER(2,(POWER(2,127)) -1

[QUOTE=Mastan;327845][B]2^primenumber -1 is always a prime number ?[/B][/QUOTE]

No, sorry. All the Mersenne numbers we are checking for primality have this form and almost all are proved to be composite in the end. So far we have only found 48 numbers of this form who are prime.

Check:

[URL]http://en.wikipedia.org/wiki/Mersenne_prime#List_of_known_Mersenne_primes[/URL]

[QUOTE=Mastan;327850]Ok, Thanks what about this .


2 ^ 2 ^127 -1 which is more clearly POWER(2,(POWER(2,127)) -1[/QUOTE]

2^p-1 iff p is prime, however the reverse p is prime iff 2^p-1 is prime is false, first counter example is 2^11-1 =23*89.

[QUOTE=Mastan;327850]Ok, Thanks what about this .

2 ^ 2 ^127 -1 which is more clearly POWER(2,(POWER(2,127)) -1[/QUOTE]

Sigh... 2 ^ 127 isn't prime. By definition.

Therefore 2 ^ 2 ^ 127 -1 isn't prime.

MM127
 

[QUOTE=Mastan;327850]2 ^ 2 ^127 -1 which is more clearly POWER(2,(POWER(2,127)) -1[/QUOTE]

I think you meant 2^(2^127-1)-1 ?

That's a so called double mersenne number. Its increadibly large and has so far not been shown to be composite.

But I am working on it :smile::

[URL]http://www.doublemersennes.org/mm127.php[/URL]

Hi ,
POWER(2,2)-1 is primenumber (3)
POWER(2,3)-1 is a primenumber (7)
POWER(2,7)-1 is a primenumber (127)
POWER(2,127)-1 is also a primenumber ( 170141183…884105727 )

so this also probably be a primenumber
POWER(2,170141183…884105727 ) -1 . Please let me know if it is really proved to be not a prime number ?

[QUOTE=aketilander;327855]Its increadibly large and has so far not been shown to be composite.

But I am working on it :smile::[/QUOTE]

and I'm rooting for you hard. You've got about a 1% chance of finding a factor with a lot more effort.

if it is a primenumber , can we conclude that 2 POWER (mersenne prime number) is always a prime number, so then we can easily figure out the next largest primenumbers .

[QUOTE=Mastan;327861]if it is a primenumber , can we conclude that 2 POWER (mersenne prime number) is always a prime number, so then we can easily figure out the next largest primenumbers .[/QUOTE]

An example of one of the many downsides of the "Slashdot effect"....