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 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. 
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 upthread. 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. 
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