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Old 2012-03-24, 15:00   #78
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Quote:
Originally Posted by science_man_88 View Post
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 ?
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Old 2012-03-24, 15:10   #79
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Quote:
Originally Posted by sascha77 View Post
"...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.

Last fiddled with by science_man_88 on 2012-03-24 at 15:12
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Old 2012-03-24, 20:37   #80
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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).
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Old 2012-03-25, 03:31   #81
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Quote:
Originally Posted by sascha77 View Post
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
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Old 2012-03-25, 04:46   #82
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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?
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Old 2012-03-26, 05:44   #83
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Quote:
Originally Posted by Dubslow View Post
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.

Last fiddled with by ATH on 2012-03-26 at 05:44
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Old 2012-03-26, 05:46   #84
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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?
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Old 2012-03-26, 07:22   #85
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Quote:
Originally Posted by Dubslow View Post
How exactly did you download all the factors?
See Will Edington's page, for example (middle of the page as *.bz2-files).
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Old 2012-03-26, 09:09   #86
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Quote:
Originally Posted by Dubslow View Post
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.
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Old 2012-03-26, 19:12   #87
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Quote:
Originally Posted by ATH View Post
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
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Old 2012-03-26, 21:16   #88
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Quote:
Originally Posted by ATH View Post
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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