Largest known k? - Page 2

jasong · 2009-07-07, 03:52

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.

TimSorbet · 2009-07-07, 12:43

Quote:

Originally Posted by jasong

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.

davieddy · 2009-07-07, 13:55

Quote:

Originally Posted by Uncwilly

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.

plandon · 2009-07-07, 15:09

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?

10metreh · 2009-07-08, 16:39

Another interesting question: What is the largest k for a factor found by TF?

plandon · 2009-07-09, 10:06

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

kar_bon · 2009-07-09, 10:23

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.

plandon · 2009-07-11, 12:55

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.

retina · 2009-07-11, 13:35

Quote:

Originally Posted by plandon

The biggest known smallest k is (M42643801-1)/(2*42643801)

Why not p=43112609? Wouldn't that be larger?

ATH · 2009-07-11, 14:25

Quote:

Originally Posted by plandon

The biggest known smallest k is (M42643801-1)/(2*42643801)

Quote:

Originally Posted by retina

Why not p=43112609? Wouldn't that be larger?

2*42643801 is not a factor of 2^42643801-2, same for p=43112609.

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

axn · 2009-07-11, 15:18

Quote:

Originally Posted by ATH

2*42643801 is not a factor of 2^42643801-2, same for p=43112609.

Really? How do you figure?

Quote:

Originally Posted by ATH

Anyway even if they were that would be a 2*k*p factor of 2^p-2. This thread is about 2*k*p+1 factors of 2^p-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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2009-07-07, 03:52	#12
jasong "Jason Goatcher" Mar 2005 6663₈ Posts	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.

2009-07-07, 15:09	#15
plandon May 2009 Loughborough, UK 2²×11 Posts	The biggest known smallest k is (M42643801-1)/(242643801) 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?*

2009-07-08, 16:39	#16
10metreh Nov 2008 912₁₆ Posts	Another interesting question: What is the largest k for a factor found by TF?

2009-07-09, 10:23	#18
kar_bon Mar 2006 Germany 2,999 Posts	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.

2009-07-11, 12:55	#19
plandon May 2009 Loughborough, UK 2²×11 Posts	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.