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Old 2009-07-07, 03:52   #12
jasong
 
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Well, people probably already thought of this, but if you simply turn the entire k*2^n+c into a raw number, you could probably beat the record rather easily. :)

Depends on whether or not you go by the rule that if k is even then you divide it by 2 and add 1 to n to get the "right" number.
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Old 2009-07-07, 12:43   #13
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Quote:
Originally Posted by jasong View Post
Well, people probably already thought of this, but if you simply turn the entire k*2^n+c into a raw number, you could probably beat the record rather easily. :)

Depends on whether or not you go by the rule that if k is even then you divide it by 2 and add 1 to n to get the "right" number.
We're talking about the k in 2kp+1 (it's proven that all factors of Mersenne numbers are of this form, for some integer k), not about the k in k*b^n+c.
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Old 2009-07-07, 13:55   #14
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Quote:
Originally Posted by Uncwilly View Post
We all know that it is not the size of the factor that counts, rather the size of the k.
Yes and no.
For trial division in ascending order,
k is a good measure of the number of factors that need to be tested,
but the difficulty of each trial division increases with the size of the factor.
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Old 2009-07-07, 15:09   #15
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The biggest known smallest k is (M42643801-1)/(2*42643801)

This thread is interesting.
What is the average k? How often is k=1?
or where is the data so that I can average it myself?
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Old 2009-07-08, 16:39   #16
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Another interesting question: What is the largest k for a factor found by TF?
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Old 2009-07-09, 10:06   #17
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Where may I find the data?

Quote:
At the bottom of the GIMPS search status page you will find links to several files:
There are no links at the bottom of that page and the link to factors.zip gives a 505 error.

How many factors should I expect to find? How big a file?

The largest factors are missing where Mx is fully factored. How can I reconstitute these factors?
Are they tagged somehow as fully factored?
The only way I could think of would be to primality test Mx/all_listed_factors_of_Mx
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Old 2009-07-09, 10:23   #18
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look here at the 1st third of the page, there you'll find files named results.pfk.split.<xx>.bz2 with all factors of Mersenne numbers.
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Old 2009-07-11, 12:55   #19
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Thanks for that.
Will Edgington stores them as k's, so that makes it easier.

It looks like the fully factored ones do have the largest factor missing and some of the smaller exponents are missing.
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Old 2009-07-11, 13:35   #20
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Quote:
Originally Posted by plandon View Post
The biggest known smallest k is (M42643801-1)/(2*42643801)
Why not p=43112609? Wouldn't that be larger?
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Old 2009-07-11, 14:25   #21
ATH
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Quote:
Originally Posted by plandon View Post
The biggest known smallest k is (M42643801-1)/(2*42643801)
Quote:
Originally Posted by retina View Post
Why not p=43112609? Wouldn't that be larger?
2*42643801 is not a factor of 242643801-2, same for p=43112609.

Anyway even if they were that would be a 2*k*p factor of 2p-2. This thread is about 2*k*p+1 factors of 2p-1.

Last fiddled with by ATH on 2009-07-11 at 14:26
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Old 2009-07-11, 15:18   #22
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Quote:
Originally Posted by ATH View Post
2*42643801 is not a factor of 242643801-2, same for p=43112609.
Really? How do you figure?

Quote:
Originally Posted by ATH View Post
Anyway even if they were that would be a 2*k*p factor of 2p-2. This thread is about 2*k*p+1 factors of 2p-1.
If you agree that M(p) is a factor of M(p), then that is exactly what this thread discusses (hint:- 2kp = M(p)-1 and 2kp+1 = M(p) are equivalent)
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