20211229, 23:14  #1 
Aug 2002
Buenos Aires, Argentina
2646_{8} Posts 
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 
20211230, 00:53  #2 
"James Heinrich"
May 2004
exNorthern Ontario
3·1,237 Posts 
Thanks, it should display a bit better now. Let me know if it's still not as expected.

20211230, 02:43  #3 
Aug 2002
Buenos Aires, Argentina
2×3×241 Posts 
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.

20211230, 03:07  #4 
"James Heinrich"
May 2004
exNorthern Ontario
3711_{10} Posts 

20211230, 03:15  #5 
Aug 2002
Buenos Aires, Argentina
2×3×241 Posts 
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. 
20211230, 04:07  #6 
"James Heinrich"
May 2004
exNorthern Ontario
7177_{8} Posts 

20211230, 04:16  #7  
Jan 2021
California
101111111_{2} Posts 
Quote:
But we certainly don't need to worry about that any time soon. 

20211230, 12:04  #8 
Aug 2002
Buenos Aires, Argentina
2·3·241 Posts 
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.

20211230, 12:05  #9  
Aug 2002
Buenos Aires, Argentina
2×3×241 Posts 
Quote:
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 20211230 at 12:28 

20211230, 14:25  #10 
"James Heinrich"
May 2004
exNorthern Ontario
3·1,237 Posts 

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