mersenneforum.org is 2^97600541752017987211-1 prime?
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 2012-08-08, 04:49 #1 devarajkandadai     May 2004 1001111002 Posts is 2^97600541752017987211-1 prime? Is 2^p-1 a Mersenne prime? Here p = 97600541752017987211 a prime number.
2012-08-08, 05:52   #2

May 2004

22×79 Posts
is2^p-1 prime?

Quote:
 Originally Posted by devarajkandadai Is 2^p-1 a Mersenne prime? Here p = 97600541752017987211 a prime number.
Looks as if 3299 is a factor; confirmation invited.

2012-08-08, 05:57   #3

May 2004

22×79 Posts
is 2^p-1 prime?

Quote:
 Originally Posted by devarajkandadai Looks as if 3299 is a factor; confirmation invited.
Sorry; the factor is 2^3299 -1. Confirmation requested.

 2012-08-08, 06:14 #4 frmky     Jul 2003 So Cal 2·3·347 Posts No, M3299 is not a factor of M97600541752017987211. Try again.
 2012-08-08, 07:21 #5 Uncwilly 6809 > 6502     """"""""""""""""""" Aug 2003 101×103 Posts 224118 Posts How did you arrive at that number? There are no factors through 2^97.
2012-08-08, 11:41   #6
alpertron

Aug 2002
Buenos Aires, Argentina

5·269 Posts

Quote:
 Originally Posted by frmky No, M3299 is not a factor of M97600541752017987211. Try again.
That's right. Since gcd(2a-1,2b-1) = 2gcd(a,b)-1 (see lemma 2 at Will Edgington Mersenne Prime which is credited to Donald Knuth), 2p-1 cannot be a multiple of 2q-1 when both p and q are prime.

2012-08-08, 13:11   #7
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26×131 Posts

Quote:
 Originally Posted by devarajkandadai Looks as if 3299 is a factor; confirmation invited.
one problem 3299 is not of form 2*k*p+1 the first possibility ( which has already been eliminated by the sounds of it) is:

195201083504035974423

 2012-08-09, 03:18 #8 devarajkandadai     May 2004 22·79 Posts is 2^p-1 prime? Agreed; that was a hasty conclusion; on recheck both are non-factors.
 2012-08-13, 05:41 #9 devarajkandadai     May 2004 22×79 Posts is 2^p - 1 prime? Whether 2^P - 1 is prime or not, all factors of 2^P - 1 seem to have the shape P*k + 1 ( here P is any prime and k belongs to N ). Hence the factors of 2^p - 1 must also have the shape 97600541752017987210*k + 1.
2012-08-13, 05:54   #10
Dubslow

"Bunslow the Bold"
Jun 2011
40<A<43 -89<O<-88

160658 Posts

Quote:
 Originally Posted by devarajkandadai Whether 2^P - 1 is prime or not, all factors of 2^P - 1 seem to have the shape P*k + 1 ( here P is any prime and k belongs to N ). Hence the factors of 2^p - 1 must also have the shape 97600541752017987210*k + 1.
It's a well known fact that all Mersenne factors are of the form 2*p*k+1. So any factors must be 2*97600541752017987210*k + 1. Someone even mentioned this a few posts up.

2012-08-13, 09:35   #11
firejuggler

Apr 2010
Over the rainbow

43·59 Posts

Quote:
 Originally Posted by Dubslow It's a well known fact that all Mersenne factors are of the form 2*p*k+1. So any factors must be 2*97600541752017987210*k + 1. Someone even mentioned this a few posts up.

97600541752017987211, maybe?

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