Reserved for MF - Sequence 4788

[kar_bon]

Originally Posted by henryzz

looking at the karsten's records page it looks like 175 digits

corrected to 173 digits!

[Raman]

How long are you going to extend the sequence 314718? Till iteration 9000? Is it getting difficult? Why don't we extend the sequence 1578 at iteration 7261? Is someone working on that number already?

[10metreh]

Originally Posted by Raman

How long are you going to extend the sequence 314718? Till iteration 9000? Is it getting difficult? Why don't we extend the sequence 1578 at iteration 7261? Is someone working on that number already?

1578 is under the control of a "driver" (2 * 3), which is a set of factors that persist and always push the sequence upwards. To escape 2 * 3, a line has to factor as 2 * 3^2 * p, where p is a prime of the form 4n+1. 4788 is not under the control of a driver, and although it is going up, there is a chance it will drop the 3 from 2^4 * 3, and then it will have a chance of acquiring the downdriver (2 * <something that isn't 3> * ....), after which it will go down. This means it has a much higher chance of terminating in the near future.

[fivemack]

4000 @ 4e7 done on the C145 from 4788:2466; time for GNFS.

I've been running a polynomial selection in parallel; won't be able to do the sieving myself, but a pretty good polynomial is

n: 2731277733959968169313770677931211293039092240425293759926078826637186378568780767241107236657396164773599806169440569332028429227856163376999057
type: gnfs
skew: 2806664.12
c0: -537701751961052562535970119801728000
c1:  1744523195224888821560862375080
c2:  1338728504837455624301882
c3: -317279220701420893
c4: -224866274934
c5:  18480
Y0: -10812700210350163142223819967
Y1:  14144226355213709
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
alambda: 2.6
rlambda: 2.6
alim: 20000000
rlim: 20000000

Siever 14e, sieve A side 10M-20M and see how much further is needed.

[bsquared]

Originally Posted by fivemack

Siever 14e, sieve A side 10M-20M and see how much further is needed.

Ok, thanks!

I'll take the whole job.

[bsquared]

prp68 factor: 45038238154540495578229005737573886297206834547447537402461361228041
prp77 factor: 60643529717749771496825937363787963901083989172307055129277826960716417883977

+ a couple more iterations. currently on a C146, for which 3k curves at 3e6 will be done in a couple hours.

[10metreh]

Originally Posted by bsquared

prp68 factor: 45038238154540495578229005737573886297206834547447537402461361228041
prp77 factor: 60643529717749771496825937363787963901083989172307055129277826960716417883977

+ a couple more iterations. currently on a C146, for which 3k curves at 3e6 will be done in a couple hours.

+ something that could be important in the future: the 3 is squared.

[Prime95]

Originally Posted by 10metreh

+ something that could be important in the future: the 3 is squared.

Pardon my newbie-like question: How will 3^2 affect the driver?

[10metreh]

Originally Posted by Prime95

Pardon my newbie-like question: How will 3^2 affect the driver?

1. 2^4 * 3 is not a driver. It is not even a guide. 2^4 is the guide.
2. When the 3 is squared, it plays no part in proceedings as far as drivers and guides, in particular powers of 2, are concerned. This makes it easier for drivers such as 2 * 3 and 2^3 * 3 to be acquired.

[Greebley]

ya, sigma(3^2) is odd, as compare to 3 itself with sigma of 4 (so 2 powers of 2).

It means for example that with the square if you get a single prime equal 1 mod 4 the power of 2 can go to 2^1. If that prime wasn't equal to 2 mod 3 (i.e. 1 mod 3) you would get the down driver. If it is 2 mod 3 then you get 2*3 which is not good because the 3 term sticks around.

With 3^1, the best you can get is 2^3 so one can't get the downdriver until the 3 term is lost or squared.

[jrk]

I started a poly search for the c146. In about 24 hours I'll post a result.