mersenneforum.org Mersenne Prime or not? (Is that a question?)
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 View Poll Results: Is M2133277 a prime? Yes 3 11.54% No 17 65.38% Dunno 2 7.69% Only in some bases 4 15.38% Voters: 26. You may not vote on this poll

 2021-05-13, 08:36 #1 SGMaths   May 2021 110 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?
2021-05-13, 11:41   #2
lycorn

Sep 2002
Oeiras, Portugal

5B716 Posts

Quote:
 Originally Posted by SGMaths 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

 2021-05-13, 11:46 #3 ZFR     Feb 2008 Bray, Ireland 151 Posts I have to say, love the poll.
2021-05-13, 12:39   #4
Dr Sardonicus

Feb 2017
Nowhere

32×509 Posts

Quote:
 Originally Posted by SGMaths 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.

 2021-05-13, 13:51 #5 kriesel     "TF79LL86GIMPS96gpu17" Mar 2017 US midwest 5,233 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 up-thread. And all Mersenne primes have primes as exponents. Last fiddled with by kriesel on 2021-05-13 at 13:54
2021-05-13, 15:27   #6
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

2·4,729 Posts

Quote:
 Originally Posted by SGMaths Does that mean M2133277 is prime?
The primality of numbers is always determined by polls.
This is a democracy, after all!

 2021-05-13, 16:19 #7 LaurV Romulan Interpreter     Jun 2011 Thailand 13·733 Posts You don't like democracy, it looks like...
2021-05-13, 18:56   #8
ZFR

Feb 2008
Bray, Ireland

15110 Posts

Quote:
 Originally Posted by Batalov The primality of numbers is always determined by polls. This is a democracy, after all!
If you don't vote, the naysayers will win.

2021-05-13, 19:15   #9
chalsall
If I May

"Chris Halsall"
Sep 2002

2·7·691 Posts

Quote:
 Originally Posted by ZFR If you don't vote, the naysayers will win.
There's no point in being pessimistic. It doesn't work, anyway...

2021-05-14, 00:39   #10
VBCurtis

"Curtis"
Feb 2005
Riverside, CA

482810 Posts

Quote:
 Originally Posted by chalsall There's no point in being pessimistic. It doesn't work, anyway...
This is gold, sir.

2021-05-14, 03:52   #11
mathwiz

Mar 2019

2·5·17 Posts

Quote:
 Originally Posted by VBCurtis This is gold, sir.
Probably just fool's gold.

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