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drummers-lowrise
1) Message boards : General discussion : Root(s) of a cubic polynomial (Message 77600)
Posted 2036 days ago by HellGauss
Thanks a lot for the reference!
2) Message boards : General discussion : Root(s) of a cubic polynomial (Message 77549)
Posted 2037 days ago by HellGauss
Just a simple question (if you know the answer...)

Is it always possible to decompose a cubic real polynomial in 3 factors of degree one each or in two factor of degree one and two, using only basic operations and n-roots?

I know about Cardano's formula, but my question is a little bit more subtle.

If the polynomial has only one real root, you can find it using Cardano's formula. Then you can easily find the other polynomial by division.

But if you have three real roots, in Cardano's formula you need to calculate the cubic root of a complex number, which, as far as I know, need trigonometric functions to obtain explicit values of the real and imaginary part.

Thanks for any insight on this problem
HG
3) Message boards : General discussion : Prime test results in genefer (Message 75127)
Posted 2118 days ago by HellGauss
I noticed that llr output (prime / not prime) is reported in my account page in the 'Is Prime?' after the quorum for the validation has been reached. This give also the informations on what number has been processed.

Is this available also for other tasks (e.g. Genefer?)

I noticed that the number which have been processed is reported on the 'task' page in the stderr output, but i cannot identify the result of the primality test.
4) Message boards : Cullen/Woodall prime search : My work units are pending (woodall) (Message 66016)
Posted 2429 days ago by HellGauss
Ok , thanks for the replies.

I am not in hurry to get credits, i just wanted to be sure that everything was right.

HG
5) Message boards : Cullen/Woodall prime search : My work units are pending (woodall) (Message 65855)
Posted 2432 days ago by HellGauss
Is it a bug? It seems that my Woodall results are not being doublechecked

http://www.primegrid.com/workunit.php?wuid=334183164
http://www.primegrid.com/workunit.php?wuid=334184604
http://www.primegrid.com/workunit.php?wuid=334265523
http://www.primegrid.com/workunit.php?wuid=334117210
6) Message boards : General discussion : Polynomial time factoring (Message 64021)
Posted 2486 days ago by HellGauss
It seems that a general polynomial-time factoring algorithm exist, although some details are still to be developed:

http://arxiv.org/abs/1212.4969
7) Message boards : Prime Sierpinski Problem : Patience, Patience (Message 64001)
Posted 2487 days ago by HellGauss
i have a 1.6GHz atom netbook. I can only run riesel sieve and llr pps on it. Other task are too long with respect to their time-out.
8) Message boards : Number crunching : New PPS Sieve run much longer same credit (Message 63794)
Posted 2495 days ago by HellGauss

One of those steps is that sometimes the sieves are going to require a quorum of 2 (or more) matching results in order to validate.


As an engineer i deal with security coefficient each day. I *strongly* agree with this choice. If the system can be cheated, someone will try to cheat, just for the sake of demonstrate that the system can be cheated.


That then implies that we'll be searching far more candidates with LLR than we really need to search.


This is actually a good thing, since this means that no prime is missed (i think that sieve task returns actual factor? So it is easy to DC sieved composite numbers?)

Since i think with a 'black hat' on my head, i also suggest you to stop the adaptive replicator on LLR, and always perform a DC also on LLR. Even if adaptive replicator makes it difficult to cheat the validator, someone could try to cheat adaptive replication, and then cheat the validator.
9) Message boards : Proth Prime Search : No available tasks (Message 62799)
Posted 2526 days ago by HellGauss
There is something strange...

My situation: i have active in the preferences only pps sieve and pps llr at this moment. On 3 of my 4 pc i receive only sieve tasks, while on the fourth PC (a very slow netbook without GPU) i receive llr.

Why?
10) Message boards : News : New LLR credit function (Message 62731)
Posted 2528 days ago by HellGauss
Just for curiosity, what is the formula? (If its simple, i wonder about some polinomial and multi-logaritmic expression...)
Is the algorithm 'writable' as a formula or is a complex algorithm?

Thanks

i.e:
how many credit for k*2^n+1? and for k*2^n-1? Is there a formula also to k^2^n+1?

Thanks!


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