Starting new bases

[gd_barnes]

Originally Posted by KEP

A final note, on the Riesel side, for some reason that I'm not aware of, k=1 is always excluded from any testings. However this is not the case on the Sierpinski side.

Regards

KEP

k=1 is considered on both sides but by definition on the Riesel side, all k=1 except base 2 have a trivial factor. See it on the pages. Examples:

Base 2 has no trivial factors so k=1 is considered but is quickly eliminated because 1*2^2-1=3 is prime.

Base 3, k=1 is eliminated with a trivial factor of 2.

Base 4, k=1 is eliminated with a trivial factor of 3.

Base 5, k=1 is eliminated with a trivial factor of 4 (actually 2).

Base 6, k=1 is eliminated with a trivial factor of 5.

(etc.)

On the Sierp side, for even bases, all k=1 make GFN's and so are not considered because many of them most likely will not have a prime, even though we cannot prove it with today's math knowledge. For odd bases, all k=1 are eliminated with a trivial factor of 2.

The effect of all of this is that k=1 only needs a prime for Riesel base 2 but that has already been found so no bases remain where k=1 needs a prime.


Gary

[rogue]

For the rieselator script, I suggest that you use the GCD function to eliminate k. For example, if b = 16, then you need to add the lines

IF (k % 3 == 1) THEN GOTO next_k
IF (k % 5 == 1) THEN GOTO next_k

What you could do is this:

SET km1, k - 1
SET bm1, b - 1
IF (GCD(km1, bm1) > 0) THEN GOTO next_k

That would make the script for any b out of the box. One would just have to modify max_k and max_n.

IIUC, for Sierpinski, these lines would be:

SET kp1, k + 1
SET bm1, b - 1
IF (GCD(kp1, bm1) > 0) THEN GOTO next_k

It should be possible to write a script that works for both Sierpinski and Riesel and have a switch that controls the +1/-1 specific code.

Thoughts?

[henryzz]

that looks brilliant rogue

it would also be very helpful if someone could add removing multiplier of base ks properly
edit: if i was completely sure about how it works i would add it myself

[rogue]

Originally Posted by henryzz

that looks brilliant rogue

it would also be very helpful if someone could add removing multiplier of base ks properly
edit: if i was completely sure about how it works i would add it myself

I'm done with the script. I have one question for Gary (in another thread) that I need him to answer before I post any scripts. I think that it is important that the script shows a proof explaining why those k can be safely skipped.

[kar_bon]

read also this thread:

there're explanations, how the MOBs work and how to implement.

especially posts #40, #43 and #58

[gd_barnes]

Ian (MyDogBuster) has sent me what appears to be a failproof script. I'm in contact with him on how to run it.

His script appears excellent. Not only will it eliminate M'sOB and k's with trivial factors, it will also work for both Riesel and Sierp, AND write out 4 separate files!! The files are:
1. Primes.
2. k's remaining.
3. k's eliminated by trivial factors.
4. k's eliminated that were MOB.

Ian, I think the only "easy" thing left is to have it automatically eliminate k's that make GFN's on the Sierp side. These would be POWERS (not multiples) of the base for even Sierp bases only. As an example, it would be k=6^0, 6^1, 6^2, 6^3, etc., i.e. k=1, 6, 36, 216, etc., for Sierp base 6.

Never fear everyone, pretty soon most new bases will be easy to start.

The only tricky ones will be bases with algebraic factors that can eliminate k's and perfect square (or greater power) bases where primes already found from smaller bases preclude us from having to search them.

Speaking of algebraic factors, it will also be very possible in the future to have a script that removes MOST k's that have algebraic factors (to make a full covering set) for k's that are perfect squares per the "generallizing algebraic factors" thread. We can't do them all at this point because we don't know them all. Some are so esoteric (i.e. very rare perfect cubes) that there's virtually no way to program for them. [See Sierp base 63 with only 2 k's that can be eliminated that are perfect cubes on a conjecture of k>37M for a good example.]


Gary

[MyDogBuster]

Gary, The script puts out 4 files, You forgot about the remaining k's file.
As I told you it is highly plagraized so thanks to all who I stole stuff from.
I think it was mainly Willem's scr.txt that I tweaked. I just looked at Scripitfy again and it is possible to code the script so that
you only tell the script whether it's Riesel or Sierp and the script will handle all the sign changes.

I created the extra files so that one could see the whole picture in front of them. I mainly wanted them so that I could insure that ALL k's were tested.

I'll look into doing that powers of the base stuff also.

[gd_barnes]

Funny thing is that I just now realized that and came on to correct it. I'm doing that now.

[gd_barnes]

BTW, it writes out a primes file like this:

39112687962150934484295053
513134110502509
19565295377
769701165753763
1026268221005017
51358900363
10518791926523
58695886129
13720163382421
21251424727068768200453
95380814959
100272138803
117391772257
24238955308943
158968024931
6902239052144282556052069
12157023826708828069803060538194761886686632539194100390158404160586945545569691991661836167062642848351274130486081632589645849
5901042270778843

Do I have a switch set wrong? I'm only using the trial factoring switch -f100. Or do you have a way to convert those into k*b^n+/-1 format?


Gary

[MyDogBuster]

Thats the pfgw-prime.txt file, the real one is pl_prime.txt.
PFGW creates the first one as some kind of work file.
I just delete it when I'm done.

[Siemelink]

Originally Posted by gd_barnes

BTW, it writes out a primes file like this:

39112687962150934484295053
513134110502509
19565295377
769701165753763
1026268221005017
51358900363
10518791926523
58695886129
13720163382421
21251424727068768200453
95380814959
100272138803
117391772257
24238955308943
158968024931
6902239052144282556052069
12157023826708828069803060538194761886686632539194100390158404160586945545569691991661836167062642848351274130486081632589645849
5901042270778843

Do I have a switch set wrong? I'm only using the trial factoring switch -f100. Or do you have a way to convert those into k*b^n+/-1 format?


Gary

This is normal. You're looking at pfgw.log, which is created by pfgw.exe. As this is undecipherable there is the file prime_found.txt that lists all the primes and PRP in the format of k*b^n-1.
I once mentioned this to Rogue if a switch could be included in his next PFGW. Our master programmer sets his own priorities so we'll see.

Willem.