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Old 2009-04-24, 07:01   #1
joblack
 
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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
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Old 2009-04-24, 10:50   #2
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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
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Old 2009-04-24, 10:54   #3
R.D. Silverman
 
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Quote:
Originally Posted by ATH View Post
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.
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Old 2009-04-24, 10:57   #4
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Quote:
Originally Posted by R.D. Silverman View Post
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.
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Old 2009-04-24, 23:29   #5
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But the OP specified p > 7. You're covered.
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Old 2009-04-25, 03:21   #6
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How about M_17 and M_19 ?
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Old 2009-05-01, 02:55   #7
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Quote:
Originally Posted by philmoore View Post
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.
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Old 2009-05-01, 10:25   #8
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Quote:
Originally Posted by joblack View Post
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
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Old 2009-05-01, 12:59   #9
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Quote:
Originally Posted by ET_ View Post
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"
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Old 2009-05-01, 15:34   #10
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Quote:
Originally Posted by ET_ View Post
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
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Old 2009-05-01, 19:52   #11
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Quote:
Originally Posted by R.D. Silverman View Post
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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