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 2009-04-24, 07:01 #1 joblack     Oct 2008 n00bville 10111000002 Posts Questions I'm wondering about the known or estimated distribution of mersenne prime numbers? Other question isn't it theoretically possible that two Mersenne Prime Numbers could occure like Mp and Mp+2 (for higher p € P, p > 7) and both could be Mersenne Prime Numbers? It seems that for higher p's the gaps between mersenne primes get bigger and bigger ... Last fiddled with by joblack on 2009-04-24 at 07:04
 2009-04-24, 10:50 #2 ATH Einyen     Dec 2003 Denmark 3×17×67 Posts Estimated distribution of Mersenne Primes: http://primes.utm.edu/notes/faq/NextMersenne.html Mp+2 (2p+1) will always be divisable by 3, so if a mersenne prime is part of a twin prime it has to be Mp-2 and Mp (2p-3 and 2p-1). Last fiddled with by ATH on 2009-04-24 at 10:50
2009-04-24, 10:54   #3
R.D. Silverman

"Bob Silverman"
Nov 2003
North of Boston

23·937 Posts

Quote:
 Originally Posted by ATH Estimated distribution of Mersenne Primes: http://primes.utm.edu/notes/faq/NextMersenne.html Mp+2 (2p+1) will always be divisable by 3, so if a mersenne prime is part of a twin prime it has to be Mp-2 and Mp (2p-3 and 2p-1).
You misconstrue. The original question was poorly posed.
The OP meant: can M_p and M_{p+2} both be prime, and not
M_p and M_p + 2.

The answer is unknown.

2009-04-24, 10:57   #4
R.D. Silverman

"Bob Silverman"
Nov 2003
North of Boston

23·937 Posts

Quote:
 Originally Posted by R.D. Silverman You misconstrue. The original question was (I believe) poorly posed. The OP meant: can M_p and M_{p+2} both be prime, and not M_p and M_p + 2. Clearly 2^n+1 is always divisible by 3 for odd n.
Correction. I forgot that M_3 and M_5 and M_7 are prime. Mea culpa.

 2009-04-24, 23:29 #5 cheesehead     "Richard B. Woods" Aug 2002 Wisconsin USA 22·3·641 Posts But the OP specified p > 7. You're covered.
 2009-04-25, 03:21 #6 philmoore     "Phil" Sep 2002 Tracktown, U.S.A. 25×5×7 Posts How about M_17 and M_19 ?
2009-05-01, 02:55   #7
joblack

Oct 2008
n00bville

25×23 Posts

Quote:
 Originally Posted by philmoore How about M_17 and M_19 ?
I have the impression that the gaps are getting (relatively) bigger and bigger and the chances for a mersenne prime twin smaller and smaller.

2009-05-01, 10:25   #8
ET_
Banned

"Luigi"
Aug 2002
Team Italia

24·3·101 Posts

Quote:
 Originally Posted by joblack I have the impression that the gaps are getting (relatively) bigger and bigger and the chances for a mersenne prime twin smaller and smaller.
Do you have a table of twin prime frequencies among prime numbers?

Luigi

2009-05-01, 12:59   #9
R.D. Silverman

"Bob Silverman"
Nov 2003
North of Boston

23×937 Posts

Quote:
 Originally Posted by ET_ Do you have a table of twin prime frequencies among prime numbers? Luigi
It is well known. See Hardy & Wright. Look up the "twin prime constant"

2009-05-01, 15:34   #10
joblack

Oct 2008
n00bville

25×23 Posts

Quote:
 Originally Posted by ET_ Do you have a table of twin prime frequencies among prime numbers? Luigi
No it was just a subjective impression by looking to the small amount of known mersenne primes.

Last fiddled with by joblack on 2009-05-01 at 15:39

2009-05-01, 19:52   #11
ET_
Banned

"Luigi"
Aug 2002
Team Italia

12F016 Posts

Quote:
 Originally Posted by R.D. Silverman It is well known. See Hardy & Wright. Look up the "twin prime constant"
I know there is one. That's the reason why I asked joblack.

But you are right, my question was not well posed here. I should have asked: "Did you look at Hardy and Wright's table of twin prime frequencies among prime numbers?"

Luigi

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