Questions

[joblack]

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 ...

[ATH]

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).

[R.D. Silverman]

Originally Posted by ATH

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).

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.

[R.D. Silverman]

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.

[cheesehead]

But the OP specified p > 7. You're covered.

[philmoore]

How about M_17 and M_19 ?

[joblack]

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.

[ET_]

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

[R.D. Silverman]

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"

[joblack]

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.

[ET_]

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