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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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Old 2021-05-13, 08:36   #1
SGMaths
 
May 2021

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Question 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?
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Old 2021-05-13, 11:41   #2
lycorn
 
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Quote:
Originally Posted by SGMaths View Post
How do I know that a Mersenne prime is a prime number?
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 Lucas-Lehmer 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 Lucas-Lehmer 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 2021-05-13 at 11:49
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Old 2021-05-13, 11:46   #3
ZFR
 
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I have to say, love the poll.
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Old 2021-05-13, 12:39   #4
Dr Sardonicus
 
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Quote:
Originally Posted by SGMaths View Post
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?
According to the PrimeNet Exponent Status report for that exponent, a verified LL test says M2133277 is in fact composite.
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Old 2021-05-13, 13:51   #5
kriesel
 
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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 up-thread.
And all Mersenne primes have primes as exponents.

Last fiddled with by kriesel on 2021-05-13 at 13:54
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Old 2021-05-13, 15:27   #6
Batalov
 
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Quote:
Originally Posted by SGMaths View Post
Does that mean M2133277 is prime?
The primality of numbers is always determined by polls.
This is a democracy, after all!
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Old 2021-05-13, 16:19   #7
LaurV
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You don't like democracy, it looks like...
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Old 2021-05-13, 18:56   #8
ZFR
 
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Quote:
Originally Posted by Batalov View Post
The primality of numbers is always determined by polls.
This is a democracy, after all!
If you don't vote, the naysayers will win.
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Old 2021-05-13, 19:15   #9
chalsall
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Quote:
Originally Posted by ZFR View Post
If you don't vote, the naysayers will win.
There's no point in being pessimistic. It doesn't work, anyway...
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Old 2021-05-14, 00:39   #10
VBCurtis
 
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Quote:
Originally Posted by chalsall View Post
There's no point in being pessimistic. It doesn't work, anyway...
This is gold, sir.
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Old 2021-05-14, 03:52   #11
mathwiz
 
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Quote:
Originally Posted by VBCurtis View Post
This is gold, sir.
Probably just fool's gold.
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