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Old 2021-12-29, 23:14   #1
alpertron
 
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Default Error in Top Mersenne exponents with the most known factors

in the following Web page: Top Mersenne exponents with the most known factors ordered by the sum of bitsize of known factors, there are errors when the Mersenne number is completely factored.

It appears that the order for these Mersenne numbers is not related to the size of the number, but to difference between the sum of bitsize of known factors (S) and the number of bits of the largest factor (L).

First Mersenne numbers shown in this Web page:

Code:
1) M31,817        S = 782.97      L = 134.15
2) M726,064,763   S = 716.13      L = 83.15
3) M4,933         S = 712.41      L = 209.92
4) M1,489         S = 1,489.00    L = 778.64      S - L = 710.36
5) M5,477         S = 693.74      L = 159.37
6) M1,151         S = 1,151.00    L = 461.05      S - L = 689.95
7) M3,911         S = 674.36      L = 198.79
8) M2,243         S = 2,243.00    L = 1,577.56    S - L = 665.44
The Mersenne numbers corresponding to items #4, #6, and #8 are completely factored. You can see that the sort is not done by decreasing values of S as expected, but by S - L (exclusively in these cases).
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Old 2021-12-30, 00:53   #2
James Heinrich
 
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Thanks, it should display a bit better now. Let me know if it's still not as expected.
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Old 2021-12-30, 02:43   #3
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I do not know if the last change you did is related or not (I could not see it in action), but it appears that today the nightly data regeneration for this report takes too long.
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Old 2021-12-30, 03:07   #4
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Quote:
Originally Posted by alpertron View Post
I do not know if the last change you did is related or not
Probably related, I made a number of changes to that file today. The regeneration process got stuck, I unstuck it and ran it manually.
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Old 2021-12-30, 03:15   #5
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It works OK now. Another error is that all probabilities greater than 99.999% should be 100% and marked in green.

I do not believe it is possible to know 99.999% of the prime factors without knowing the complete factorization.
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Old 2021-12-30, 04:07   #6
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Quote:
Originally Posted by alpertron View Post
all probabilities greater than 99.999% should be 100% and marked in green.
Hmm, I thought I had fixed that before, I missed a place where it could get reset during the daily update. I've fixed it again (permanently this time, I hope).
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Old 2021-12-30, 04:16   #7
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Quote:
Originally Posted by alpertron View Post
It works OK now. Another error is that all probabilities greater than 99.999% should be 100% and marked in green.

I do not believe it is possible to know 99.999% of the prime factors without knowing the complete factorization.
Well, if the number has 100000 or more factors...
But we certainly don't need to worry about that any time soon.
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Old 2021-12-30, 12:04   #8
alpertron
 
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Quote:
Originally Posted by slandrum View Post
Well, if the number has 100000 or more factors...
But we certainly don't need to worry about that any time soon.
The current record is 12 prime factors. But even if we knew 100000 prime factors of the Mersenne number, the probability that the largest prime factor has the same size as the smallest prime factor is virtually zero.
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Old 2021-12-30, 12:05   #9
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Quote:
Originally Posted by James Heinrich View Post
Hmm, I thought I had fixed that before, I missed a place where it could get reset during the daily update. I've fixed it again (permanently this time, I hope).
It works OK now. Thanks a lot.

There is a problem in the same page if I sort by "Largest factor (bits)". For Mersenne numbers completely factored, your script is using S - L as the key for sorting as happened when the table was sorted by "Sum Bitsize of Known Factors" (that you already fixed).

Last fiddled with by alpertron on 2021-12-30 at 12:28
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Old 2021-12-30, 14:25   #10
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Quote:
Originally Posted by alpertron View Post
There is a problem in the same page if I sort by "Largest factor (bits)".
Should be fixed now.
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