mersenneforum.org Mersenne Prime or not? (Is that a question?)
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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

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

7×11×19 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

43×107 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 24×7×47 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

946510 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 32·1,061 Posts You don't like democracy, it looks like...
2021-05-13, 18:56   #8
ZFR

Feb 2008
Bray, Ireland

151 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

5×7×277 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

33·179 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

101010112 Posts

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

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