
View Poll Results: Is M2133277 a prime?  
Yes  3  11.11%  
No  18  66.67%  
Dunno  2  7.41%  
Only in some bases  4  14.81%  
Voters: 27. You may not vote on this poll 

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20210513, 08:36  #1 
May 2021
1_{16} Posts 
Mersenne Prime or not? (Is that a question?)
How do I know that a Mersenne prime is a prime number? For example, I tested M2133277 and the result was 7 curves, B1=50000, B2=50000. Does that mean M2133277 is prime?

20210513, 11:41  #2 
"GIMFS"
Sep 2002
Oeiras, Portugal
2·3^{2}·83 Posts 
Well, if it is a Mersenne prime, than it has to prime, right?
I think your meaning was "How do I know that a Mersenne number is prime?" For a Mersenne number to be prime, it has to successfully pass a primality test, like the LucasLehmer test used by GIMPS. What you have done was a search for factors. Should you have found one, you could be sure the number wasn´t prime, as it had at least a factor. As you didn´t find a factor, the number might in theory be prime. But only a primality test would tell. In this particular case, the number has already been LucasLehmer tested (and double checked) by GIMPS, so we know it is not prime. There are factor(s) waiting to be found, it is a matter of keep trying. Many of us in this community search for factors of numbers we know for sure aren´t prime. Last fiddled with by lycorn on 20210513 at 11:49 
20210513, 11:46  #3 
Feb 2008
Bray, Ireland
2×79 Posts 
I have to say, love the poll.

20210513, 12:39  #4  
Feb 2017
Nowhere
4,987 Posts 
Quote:


20210513, 13:51  #5 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
5·13·89 Posts 
Easiest way for Mersenne numbers with exponents below 55,000,000 is to check here.
And, by definition, all Mersenne primes are prime, as stated upthread. And all Mersenne primes have primes as exponents. Last fiddled with by kriesel on 20210513 at 13:54 
20210513, 15:27  #6 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
7×1,367 Posts 

20210513, 16:19  #7 
Romulan Interpreter
Jun 2011
Thailand
2634_{16} Posts 
You don't like democracy, it looks like...

20210513, 18:56  #8 
Feb 2008
Bray, Ireland
10011110_{2} Posts 

20210513, 19:15  #9 
If I May
"Chris Halsall"
Sep 2002
Barbados
10011011100010_{2} Posts 

20210514, 00:39  #10 
"Curtis"
Feb 2005
Riverside, CA
19×263 Posts 

20210514, 03:52  #11 
Mar 2019
2^{3}×5^{2} Posts 

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