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?

[QUOTE=SGMaths;578314]How do I know that a Mersenne prime is a prime number? [/QUOTE]

Well, if it is a Mersenne [B]prime[/B], than it has to prime, right?
I think your meaning was "How do I know that a Mersenne [B]number[/B] 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.

I have to say, love the poll.

[QUOTE=SGMaths;578314]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?[/QUOTE]According to the [url=https://www.mersenne.org/report_exponent/?exp_lo=2133277&exp_hi=&full=1]PrimeNet Exponent Status report[/url] for that exponent, a verified LL test says M2133277 is in fact composite.

Easiest way for Mersenne numbers with exponents below 55,000,000 is to check [URL="https://www.mersenne.org/primes/"]here[/URL].
And, by definition, all Mersenne primes are prime, as stated up-thread.
And all Mersenne primes have [URL="https://www.mersenneforum.org/showpost.php?p=512813&postcount=4"]primes as exponents[/URL].

[QUOTE=SGMaths;578314]Does that mean M2133277 is prime?[/QUOTE]
The primality of numbers is [I]always [/I]determined by polls.
This is a democracy, after all! :furious:

You don't like democracy, it looks like... :razz:

[QUOTE=Batalov;578344]The primality of numbers is [I]always [/I]determined by polls.
This is a democracy, after all! :furious:[/QUOTE]

If you don't vote, the naysayers will win.

[QUOTE=ZFR;578353]If you don't vote, the naysayers will win.[/QUOTE]

There's no point in being pessimistic. It doesn't work, anyway...

[QUOTE=chalsall;578354]There's no point in being pessimistic. It doesn't work, anyway...[/QUOTE]

This is gold, sir.

[QUOTE=VBCurtis;578367]This is gold, sir.[/QUOTE]

Probably just fool's gold.