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Old 2007-06-05, 20:37   #1
Xordan
 

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Default Mersenne exponents

Hello:
I have a query regarding the mersenne primes that I hope it is not trivial and don't have been responded many times:
There are 3 Known Mersenne primes that are also exponents of Mersenne primes: 7,31 and 127. -
Does exist some conjecture, theorem, hypothesis that says the other Mersenne primes are not or could not be Mersenne primes exponents ?
Does it exist some investigation or project on this matter?

Thank you.

Xordan
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Old 2007-06-06, 00:58   #2
cheesehead
 
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"Richard B. Woods"
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Quote:
Originally Posted by Xordan View Post
Hello:
I have a query regarding the mersenne primes that I hope it is not trivial and don't have been responded many times:
Xordan,

It is not trivial but many other people have previously thought of it and asked it.

Quote:
There are 3 Known Mersenne primes that are also exponents of Mersenne primes: 7,31 and 127. -
Does exist some conjecture, theorem, hypothesis that says the other Mersenne primes are not or could not be Mersenne primes exponents ?
There is no theorem. It is already known that the answer is: "in some cases -- yes, and in other cases -- no, but in most cases -- we don't know yet".

To find more information on this subject, search on "double Mersenne prime" or "double Mersenne number".

Quote:
Does it exist some investigation or project on this matter?
Yes. There is particular interest now in MM61 (= 2M61-1 = 22[sup]61-1[/sup]-1) and MM127 (= 2M127-1 = 22[sup]127-1[/sup]-1 = 22[sup]2[sup]7-1[/sup]-1[/sup]-1). Search on "MM127" or MM61" to find relevant sites.

Last fiddled with by cheesehead on 2007-06-06 at 01:01
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Old 2007-06-06, 02:25   #3
Mini-Geek
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"Tim Sorbera"
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Quote:
Originally Posted by cheesehead View Post
Xordan,

It is not trivial but many other people have previously thought of it and asked it.

There is no theorem. It is already known that the answer is: "in some cases -- yes, and in other cases -- no, but in most cases -- we don't know yet".

To find more information on this subject, search on "double Mersenne prime" or "double Mersenne number".

Yes. There is particular interest now in MM61 (= 2M61-1 = 22[sup]61-1[/sup]-1) and MM127 (= 2M127-1 = 22[sup]127-1[/sup]-1 = 22[sup]2[sup]7-1[/sup]-1[/sup]-1). Search on "MM127" or MM61" to find relevant sites.
I prefer to call MM127 MMMMM2 or M170141183460469231731687303715884105727.
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Old 2007-06-07, 13:40   #4
m_f_h
 
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Feb 2007

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Quote:
Originally Posted by Mini-Geek View Post
I prefer to call MM127 MMMMM2 or M170141183460469231731687303715884105727.
I prefer MM127. How about a poll ? ;-)
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Old 2007-06-07, 16:05   #5
mfgoode
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Quote:
Originally Posted by m_f_h View Post
I prefer MM127. How about a poll ? ;-)


AFAIK the notation MM127 and others like it is widely used by authors and is popular.

Mally
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