is 2^97600541752017987211-1 prime?

devarajkandadai · 2012-08-08, 04:49

Is 2^p-1 a Mersenne prime? Here p =

97600541752017987211 a prime number.

devarajkandadai · 2012-08-08, 05:52

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.

devarajkandadai · 2012-08-08, 05:57

Quote:

Originally Posted by devarajkandadai

Looks as if 3299 is a factor; confirmation invited.

Sorry; the factor is 2^3299 -1. Confirmation requested.

frmky · 2012-08-08, 06:14

No, M3299 is not a factor of M97600541752017987211. Try again.

Uncwilly · 2012-08-08, 07:21

How did you arrive at that number?

There are no factors through 2^97.

alpertron · 2012-08-08, 11:41

Quote:

Originally Posted by frmky

No, M3299 is not a factor of M97600541752017987211. Try again.

That's right. Since gcd(2^a-1,2^b-1) = 2^gcd(a,b)-1 (see lemma 2 at Will Edgington Mersenne Prime which is credited to Donald Knuth), 2^p-1 cannot be a multiple of 2^q-1 when both p and q are prime.

science_man_88 · 2012-08-08, 13:11

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

devarajkandadai · 2012-08-09, 03:18

Agreed; that was a hasty conclusion; on recheck both are non-factors.

devarajkandadai · 2012-08-13, 05:41

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.

Dubslow · 2012-08-13, 05:54

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.

firejuggler · 2012-08-13, 09:35

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?

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.

2012-08-09, 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 Pk + 1 ( here P is any prime and k belongs to N ). Hence the factors of 2^p - 1 must also have the shape 97600541752017987210k + 1.

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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.