20090424, 07:01  #1 
Oct 2008
n00bville
1011100000_{2} 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 20090424 at 07:04 
20090424, 10:50  #2 
Einyen
Dec 2003
Denmark
3×17×67 Posts 
Estimated distribution of Mersenne Primes:
http://primes.utm.edu/notes/faq/NextMersenne.html M_{p}+2 (2^{p}+1) will always be divisable by 3, so if a mersenne prime is part of a twin prime it has to be M_{p}2 and M_{p} (2^{p}3 and 2^{p}1). Last fiddled with by ATH on 20090424 at 10:50 
20090424, 10:54  #3  
"Bob Silverman"
Nov 2003
North of Boston
2^{3}·937 Posts 
Quote:
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. 

20090424, 10:57  #4 
"Bob Silverman"
Nov 2003
North of Boston
2^{3}·937 Posts 
Correction. I forgot that M_3 and M_5 and M_7 are prime. Mea culpa.

20090424, 23:29  #5 
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}·3·641 Posts 
But the OP specified p > 7. You're covered.

20090425, 03:21  #6 
"Phil"
Sep 2002
Tracktown, U.S.A.
2^{5}×5×7 Posts 
How about M_17 and M_19 ?

20090501, 02:55  #7 
Oct 2008
n00bville
2^{5}×23 Posts 

20090501, 10:25  #8 
Banned
"Luigi"
Aug 2002
Team Italia
2^{4}·3·101 Posts 

20090501, 12:59  #9 
"Bob Silverman"
Nov 2003
North of Boston
2^{3}×937 Posts 

20090501, 15:34  #10 
Oct 2008
n00bville
2^{5}×23 Posts 
No it was just a subjective impression by looking to the small amount of known mersenne primes.
Last fiddled with by joblack on 20090501 at 15:39 
20090501, 19:52  #11  
Banned
"Luigi"
Aug 2002
Team Italia
12F0_{16} Posts 
Quote:
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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