Problem of the Month - Page 8

sascha77 · 2012-03-24, 15:00

Quote:

Originally Posted by science_man_88

2*m*p+1 | 2^p-1 so really all your asking is can 2*m*p+1 divide 2 Mersennes but with only one p m=k*p is what you can check for.

"...so really all your asking is can 2*m*p+1 divide 2 Mersennes"
Sorry. But I do not quite understand what you mean.
Can you give me an example ?

science_man_88 · 2012-03-24, 15:10

Quote:

Originally Posted by sascha77

"...so really all your asking is can 2*m*p+1 divide 2 Mersennes"
Sorry. But I do not quite understand what you mean.
Can you give me an example ?

no your question becomes:

2*m*p+1 ; m=k*p does 2*m*p+1 | 2^p-1 replace p with q in m=k*p and we have the 2 Mersennes problem talked about before.

Dubslow · 2012-03-24, 20:37

No, I don't believe so. What he is asking is if there is any factor where n in 2np+1 itself has a factor of p. @sascha: http://mersenne-aries.sili.net keeps a database similar to PrimeNet except that it shows you detailed information about any factors known, including factoring the n in 2np+1 automatically (though the most common notation calls it k, not n).

ATH · 2012-03-25, 03:31

Quote:

Originally Posted by sascha77

Is it possible to chose p and k as descibed in (1) and (2), so that
$2*k*p^{2}+1$ is prime and satisfies the congruence:

$2^p \equiv 1 \;\;(\;mod\; 2*k*p^{2}+1\;)$

Works with: p=93077, k=674487

http://www.mersenne.org/report_expon...&B1=Get+status

Dubslow · 2012-03-25, 04:46

And the equivalent page from the site I showed you:
http://mersenne-aries.sili.net/expon...tdetails=93077

ATH, how did you find it that fast?

ATH · 2012-03-26, 05:44

Quote:

Originally Posted by Dubslow

ATH, how did you find it that fast?

I had a text file with a lot of GIMPS factors lying around and I just made a program to quickly check if factor-1 = 0 (mod p^2).

I now downloaded, I think, the entire GIMPS factor database: 33,545,802 factors up to p=1,000,000,000, and there is NO other example besides p=93077, so this seems to be very rare indeed.

All factors of mersenne numbers are of the form 2kp+1, so this case is when k happens to be a multiple of p as well: k=c*p.

Dubslow · 2012-03-26, 05:46

Hmm... James' site goes beyond 1B, and there are definitely some factors know greater than M3.32B...
How exactly did you download all the factors?

kar_bon · 2012-03-26, 07:22

Quote:

Originally Posted by Dubslow

How exactly did you download all the factors?

See Will Edington's page, for example (middle of the page as *.bz2-files).

ATH · 2012-03-26, 09:09

Quote:

Originally Posted by Dubslow

Hmm... James' site goes beyond 1B, and there are definitely some factors know greater than M3.32B...
How exactly did you download all the factors?

I created a script that downloaded them in chunks from the server here:
http://www.mersenne.org/report_facto...B1=Get+Factors

If you want the factors you can get them from me, so we don't strain the database again for the same factors.

sascha77 · 2012-03-26, 19:12

Quote:

Originally Posted by ATH

I created a script that downloaded them in chunks from the server here:
http://www.mersenne.org/report_facto...B1=Get+Factors

If you want the factors you can get them from me, so we don't strain the database again for the same factors.

Great work !!!
I wanted today to check manually all the factors from the http://mersenne-aries.sili.net site. But you and Dubslow were faster and really found a counterexample. Great.
ATH: Can you send the file with the factors to me also ?

thanks in advance

Dubslow · 2012-03-26, 21:16

Quote:

Originally Posted by ATH

I created a script that downloaded them in chunks from the server here:
http://www.mersenne.org/report_facto...B1=Get+Factors

If you want the factors you can get them from me, so we don't strain the database again for the same factors.

Ah, I didn't realize PrimeNet had a known factors report. I was thinking you wrote a script to parse the report_exponent, but that seemed like a lot of effort

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2012-03-24, 20:37	#80
Dubslow Basketry That Evening! "Bunslow the Bold" Jun 2011 40<A<43 -89<O<-88 3×29×83 Posts	No, I don't believe so. What he is asking is if there is any factor where n in 2np+1 itself has a factor of p. @sascha: http://mersenne-aries.sili.net keeps a database similar to PrimeNet except that it shows you detailed information about any factors known, including factoring the n in 2np+1 automatically (though the most common notation calls it k, not n).

2012-03-25, 04:46	#82
Dubslow Basketry That Evening! "Bunslow the Bold" Jun 2011 40<A<43 -89<O<-88 3·29·83 Posts	And the equivalent page from the site I showed you: http://mersenne-aries.sili.net/expon...tdetails=93077 ATH, how did you find it that fast?

2012-03-26, 05:46	#84
Dubslow Basketry That Evening! "Bunslow the Bold" Jun 2011 40<A<43 -89<O<-88 3×29×83 Posts	Hmm... James' site goes beyond 1B, and there are definitely some factors know greater than M3.32B... How exactly did you download all the factors?