Possibly 41th Mersenne prime found!

[Mystwalker]

I'm not sure if everyone already knows:

GIMPS reported that they have possibly discovered the 41st known Mersenne Prime.

Now the big quiz:
How big this number is? :)

Hint: Divide n by 3.32 to get the number digits of that number.

[Keroberts1]

it might not even be the 41st perhaps it is smaller than the last one they found although chances are ita gonna be around 6800000 digits maybe even over 10,00,000 I believe they have a few people testing in that range.

[Keroberts1]

it says on the site that they have performed additional quick checks to confirm it is almost definatly a prime. What are these quick checks?

[Mystwalker]

Originally posted by Keroberts1
it might not even be the 41st perhaps it is smaller than the last one they found although chances are ita gonna be around 6800000 digits maybe even over 10,00,000 I believe they have a few people testing in that range.

Right, I forgot a "known" --> 41st known Mersenne Prime possibly found. :cry: --> Fixed it as good as I could.
The current status of the project can be seen here (http://www.mersenne.org/status.htm) . There seem to have already been approx. 10,000 tests of numbers with > 10,000,000 digits.


it says on the site that they have performed additional quick checks to confirm it is almost definatly a prime. What are these quick checks?

Looking if the number is odd or even? :D
Seriously, I have no idea and am also interested into this topic...

[wblipp]

Originally posted by Keroberts1
it says on the site that they have performed additional quick checks to confirm it is almost definatly a prime. What are these quick checks?

http://www.mersenneforum.org/showpost.php?p=29158&postcount=28

In the above message George Woltman wrote


BTW, it is a new prime. The user sent in his save file. I reran the final 15,000 iterations and prime95 rediscovered the prime. There is no known method for creating a bogus save file that falsely rediscovers the prime.

[Keroberts1]

hopefully they don't have a 10,000,000 digit prime. Maybe we could still beat them there.

[wirthi]

There is no known method for creating a bogus save file that falsely rediscovers the prime.I know there are strange people but why should someone try to fake a prime? Everybody knows the results are doublechecked. There is no sense in trying to fake.

[vjs]

People we should all be very happy that they found another prime, are we not all gaining as a species?

Also is there a possibility that this prime fits one of our potential primes?

(2^p)-1 = prime number = k.2^n+1 (for one of our k,n pairs that we have not tested)

Also another approach:

We are currently testing k,n's that fit the form k.2^n+1 and our smallest prime could be of the form (4847, 5000000) or larger (assuming we didn't make a mistake earlier)which would be at least x digits long.

So if there are primes that are larger than x digits long do we check those see if they fit a potential K,N pair? I think we should...

Wouldn't it be very silly if used 4 years of project time to finally find a known prime.

My understanding of the project is we don't really need to find the smallest prime that fits n for every k, just one prime that fits every k.

Does anyone know???

VJS

Not sure if the math works here but don't you simply:

(Take the prime number) +1 then divide by each k to see if it produces an interger number.....

Comments

[Ken_g6[TA]]

Originally posted by vjs
Also is there a possibility that this prime fits one of our potential primes?

(2^p)-1 = prime number = k.2^n+1 (for one of our k,n pairs that we have not tested)

Also another approach:

We are currently testing k,n's that fit the form k.2^n+1 and our smallest prime could be of the form (4847, 5000000) or larger (assuming we didn't make a mistake earlier)which would be at least x digits long.

So if there are primes that are larger than x digits long do we check those see if they fit a potential K,N pair? I think we should...

Wouldn't it be very silly if used 4 years of project time to finally find a known prime.

My understanding of the project is we don't really need to find the smallest prime that fits n for every k, just one prime that fits every k.

Does anyone know???

VJS

Not sure if the math works here but don't you simply:

(Take the prime number) +1 then divide by each k to see if it produces an interger number.....

Comments
In binary, numbers of the two forms look very different. 2^p-1 is a binary repunit:

11111111...1111111

whereas k*2^n+1 is
K (xxxx) *2^n (10000...0000) +1, or

xxxx0000...0001

They would only match up when k=2^(p-1)-1 and n=1.

[Keroberts1]

thye've confirmed it its 7,235,733 digits. Thye sure are getting close to the 10,000,000 mark. Guess they'll be past the boundary in about a year and a half. Probably find one wihtin two and a half years.