Gratuitous factors thread

[kenta]

Ah, I was not aware of FactorDB. Can it be made indexable by search engines? Currently its robots.txt is set to "User-agent: * Disallow: /".

I had done a Google search of the smaller known factors to see if anyone had factored C158, and afterwards a Google search of the new factor.

[lorgix]

I don't think that's realistic; it has over 668 million entries.

[Mini-Geek]

Originally Posted by kenta

Ah, I was not aware of FactorDB. Can it be made indexable by search engines? Currently its robots.txt is set to "User-agent: * Disallow: /".

I had done a Google search of the smaller known factors to see if anyone had factored C158, and afterwards a Google search of the new factor.

Originally Posted by lorgix

I don't think that's realistic; it has over 668 million entries.

Besides the raw number of entries it has, loading a page can cause the DB server/workers to do some work; I shudder to think of all the needless work that would be done due to Google crawling the site. That may be the primary reason that it blocks bots.

[firejuggler]

Enter a number in factordb ; if it is not factored, there is a 70 to 80% chance that *nobody* factored it.
We are number-hunter here, and you can be sure that any notable factorisation won't pass unnoticced. Any number below 70 digit is a quasi-instant factorisation; betwween 70-110, rarely more than 48 hours. Above... well Thats when the long wait start. But, if the factor is a special form, there is a huge chance it will be factorised soon.

[lorgix]

I've been working on HP₆(96) for a few weeks now.

ECM just found a factor of HP₆(96); n=119, c163.

c163 = p61*p103

p61 = 3797542193934420748318216003198150130484669973132741708190491

[ <2, 3>, <3, 2>, <5, 1>, <3049, 1>, <13187, 1>, <159349, 1>, <741787, 1>,
<1549157, 1>, <12702929, 1>, <12771103, 1>, <49781213, 1>, <177408706571, 1> ]

Just about to be GNFSed.

... This went in the wrong "Gratuitous factors"-thread. Helpful mod?

[jcrombie]

Here is a p50 with a fairly low B1 value.

ecm -v -inp 573_274p1 -sigma 377260338 250e3
GMP-ECM 6.4.3 [configured with GMP 5.0.5, --enable-asm-redc] [ECM]
Running on Octacore
Input number is 26594617765169572082971186497599854207008541536487789341135112181948450766499302907792912801082364687289593974376583589304816291501827306819614877594808069179709746434215653036170139495530340927783003444037007979978227755605400186955962673583857757727974515227791006582999382350373421718210600906156246369388191593106305004679192483584237106923010104204605305946934316809128902959406870355549430251967928493796191017315108754907899751201767880440133257626207914651545490882364302281118835838193847794373672875166296590346777068924215678114569160413328727496622279062959554636879435169358604054561252888130959723154678994679089377536945369419538112362590691679727964422496457202609177293526087726710399547207630373348255941 (722 digits)
Using mpz_mod
Using B1=250000, B2=183032866, polynomial Dickson(3), sigma=377260338
dF=2880, k=2, d=30030, d2=17, i0=-8
Expected number of curves to find a factor of n digits:
35    40    45    50    55    60    65    70    75    80
4550    64790    1126804    2.3e+07    5.3e+08    1.4e+10    2.1e+13    3.1e+18    4.1e+23    Inf

....

********** Factor found in step 2: 57386241110690372064202391421418864164831605741773

[lorgix]

That may very well be the largest one ever found with that B1. Certainly the largest one I've heard of.

[jcrombie]

Here is the group order thanks to factordb :

2^5 · 3^5 · 5^2 · 7^2 · 59 · 263 · 331 · 1319 · 1543 · 1783 · 2111 · 17987 · 214483 · 245039 · 161972977

So, not much room for the B1 or B2.

@lorgix I see your p49 from Nov. could of gone much lower than mine.

[xilman]

Originally Posted by jcrombie

Here is a p50 with a fairly low B1 value.

ecm -v -inp 573_274p1 -sigma 377260338 250e3
GMP-ECM 6.4.3 [configured with GMP 5.0.5, --enable-asm-redc] [ECM]
Running on Octacore
Input number is 26594617765169572082971186497599854207008541536487789341135112181948450766499302907792912801082364687289593974376583589304816291501827306819614877594808069179709746434215653036170139495530340927783003444037007979978227755605400186955962673583857757727974515227791006582999382350373421718210600906156246369388191593106305004679192483584237106923010104204605305946934316809128902959406870355549430251967928493796191017315108754907899751201767880440133257626207914651545490882364302281118835838193847794373672875166296590346777068924215678114569160413328727496622279062959554636879435169358604054561252888130959723154678994679089377536945369419538112362590691679727964422496457202609177293526087726710399547207630373348255941 (722 digits)
Using mpz_mod
Using B1=250000, B2=183032866, polynomial Dickson(3), sigma=377260338
dF=2880, k=2, d=30030, d2=17, i0=-8
Expected number of curves to find a factor of n digits:
35    40    45    50    55    60    65    70    75    80
4550    64790    1126804    2.3e+07    5.3e+08    1.4e+10    2.1e+13    3.1e+18    4.1e+23    Inf

....

********** Factor found in step 2: 57386241110690372064202391421418864164831605741773

Impressive! Have you told the other Paul about it?

[jcrombie]

Originally Posted by xilman

Impressive! Have you told the other Paul about it?

Done.

[swishzzz]

Run 709 out of 1540:
Using B1=18000000, B2=58560416470, polynomial Dickson(12), sigma=1:3576746370
Step 1 took 231256ms
Step 2 took 75816ms
********** Factor found in step 2: 26759964491830480636236398774973830719679139755537527
Found probable prime factor of 53 digits: 26759964491830480636236398774973830719679139755537527
Probable prime cofactor ((2^703+5)/49/6845413455238801142000974327019)/26759964491830480636236398774973830719679139755537527 has 127 digits

How do I find the group order for this factorization? factordb's group order calculator clearly fails for this one...