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Old 2012-08-08, 04:49   #1
devarajkandadai
 
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Minus is 2^97600541752017987211-1 prime?

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

97600541752017987211 a prime number.
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Old 2012-08-08, 05:52   #2
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Quote:
Originally Posted by devarajkandadai View Post
Is 2^p-1 a Mersenne prime? Here p =

97600541752017987211 a prime number.
Looks as if 3299 is a factor; confirmation invited.
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Old 2012-08-08, 05:57   #3
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Quote:
Originally Posted by devarajkandadai View Post
Looks as if 3299 is a factor; confirmation invited.
Sorry; the factor is 2^3299 -1. Confirmation requested.
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Old 2012-08-08, 06:14   #4
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No, M3299 is not a factor of M97600541752017987211. Try again.
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Old 2012-08-08, 07:21   #5
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How did you arrive at that number?


There are no factors through 2^97.
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Old 2012-08-08, 11:41   #6
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Quote:
Originally Posted by frmky View Post
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.
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Old 2012-08-08, 13:11   #7
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Quote:
Originally Posted by devarajkandadai View Post
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
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Old 2012-08-09, 03:18   #8
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Default is 2^p-1 prime?

Agreed; that was a hasty conclusion; on recheck both are non-factors.
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Old 2012-08-13, 05:41   #9
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Default 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.
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Old 2012-08-13, 05:54   #10
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Quote:
Originally Posted by devarajkandadai View Post
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.
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Old 2012-08-13, 09:35   #11
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Quote:
Originally Posted by Dubslow View Post
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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