100 Most Wanted

[Citrix]

I am interested in developing new factoring methods. In order to try these methods out I am looking for 100 candidates with different sizes having different size factors. If any one has any suggestions or has some candidates please post the numbers below. The problem working with some of the numbers that everyone is trying to factor is that they are hard to factor and an undeveloped method has little chance to factor them and hence we can’t figure out the power of the new factoring algorithm.

Citrix

[xilman]

Originally posted by Citrix
I am interested in developing new factoring methods. In order to try these methods out I am looking for 100 candidates with different sizes having different size factors. If any one has any suggestions or has some candidates please post the numbers below. The problem working with some of the numbers that everyone is trying to factor is that they are hard to factor and an undeveloped method has little chance to factor them and hence we can’t figure out the power of the new factoring algorithm.

Citrix

I suggest that you first develop your algorithms on integers for which you already know the factors --- because in this way you can create targets which have exactly known properties.

When you have something that seems to work on numbers of a particular size, then work on numbers of a similar size with unknown factorizations.

If you don't want to practice beforehand, there are any number of
tables of integers to be found. My web site at http://research.microsoft.com/~pleyl...ation/main.htm and links therein contains many thousands of such numbers.


Paul

[wblipp]

It's going to be hard to find numbers that people think of as "most wanted" but that haven't already had substantial attempts using ECM and perhaps P-1 and P+1.

If suitable, I'd be glad to provide composite numbers from ElevenSmooth. The ECM Server for the ElevenSmooth project has 63 active composites. These range in size from 149 digits to 6936 digits. The C149 is presently testing for 50 digit factors (B1=43M). There are 22 numbers presently testing for 40 digit factors (B1=3M), ranging from 186 to 443 digits. The numbers between 490 and 1357 digits are being tested for 35 digit factors, the larger numbers are being tested for 30 digit factors.

There are also about 100 composites that are presently being tested for 25 digit factors by the Special Project. The smallest of these are probably in the low 200 digits.

I count the C149 as my "most wanted," but would be pleased to have factors for any of these. If any these meet your requirements, I'd be glad to provide the composites.

[Citrix]

I could use these as a start and update the list as more people submit numbers. Post about 100 numbers below or PM them to me.

Thanks,
Citrix

[wblipp]

Originally posted by Citrix
Post about 100 numbers below

The ElevenSmooth FAQ now answers What composites are being distributed by the ECM Server? with a link to a text file containing the 63 composites.

[dsouza123]

31074182404900437213507500358885679300373460228427
27545720161948823206440518081504556346829671723286
78243791627283803341547107310850191954852900733772
4822783525742386454014691736602477652346609

RSA 640




You could verify your factoring method works using the recently factored RSA 576

18819881292060796383869723946165043980716356337941
73827007633564229888597152346654853190606065047430
45317388011303396716199692321205734031879550656996
221305168759307650257059

[tom11784]

Originally posted by dsouza123
You could verify your factoring method works using the recently factored RSA 576

18819881292060796383869723946165043980716356337941
73827007633564229888597152346654853190606065047430
45317388011303396716199692321205734031879550656996
221305168759307650257059

Recently factored? Their website http://www.rsasecurity.com/rsalabs/c...rs.html#RSA576 still have it as not factored.

[smh]

Recently factored? Their website http://www.rsasecurity.com/rsalabs/...ers.html#RSA576 still have it as not factored.

That shows how recentely it was

[TauCeti]

Originally posted by tom11784
Recently factored? Their website http://www.rsasecurity.com/rsalabs/c...rs.html#RSA576 still have it as not factored.

Well, it was factored involving germany. Maybe 'old europe' countries are no longer allowed to factor and the results are ignored?

Maybe US researchers even have to look for different factors of RSA-576 to abide the law?

[Citrix]

I am looking for all the factors of mersenne numbers under 2^256-1.
that is 2^n-1, n from 1 to 256

Could you please provide me with a website where I can download these
numbers.

Thanks,
Citrix

[nfortino]

Although you have to write a program to reconstruct all factors for each number,The Cunningham Project Site should have everything you need.