[quote=KEP;168214]I found the primelist for sierpinski base=5, now please tell me how to convert a k*5^n+1 prime to a k*25^+1

Is it like I think, that I have to either divide or multiply the k value and then keep the n-value the same?

Kenneth[/quote]

No and that is why I am concerned because your list of k-values that you removed is not only incomplete, it is incorrect.

Think about it mathematically. If you have a base to a huge power multiplied by a k-value, if you multiply the base by 5, there's nothing you could do to the k-value to make it small enough to end up with the same value. Sure, you could have some teeny fraction for a k-value but the conjectures only allow for integers > 0.

If you square the base, you have to divide the exponent (n-value) by 2.

There are 2 possibilities:

1. If the base 5 n-value is even, keep the k-value the same and divide the n-value by 2.

2. If the base 5 n-value is odd, multipy the k-value by 5, subtract 1 from the n-value, and then divide the resultant n-value by 2.


That is:

Where n is even:
k*5^n = k*25^(n/2)

Where n is odd:
k*5^n = 5k*25^[(n-1)/2]


Therefore your list of k's that you removed was wrong. For base 5 primes with even n-values, you must divide the n by 2 instead of multiplying the k by 5. The converted k-values would have been correct if the base 5 n-values were odd. That means the k-values that you are searching are missing the k's that you thought you had a "converted" base 5 prime for.


Here is my suggested attack method:
[code]
1. Run PFGW up to n=5000 for all k==(0 mod 6).
2. Run PFGW up to n=5000 for all k==(4 mod 6).
3. Remove k's that are divisible by 25 and where k+1 is prime (removes appropriate multiples of the base).
4. Copy-and-paste the Sierp base 5 prime list into a spreadsheet and do the following:
a. Sort them by n-value.
b. Remove all n<=10000 (because we'll be dividing the exponent by 2 in #5).
c. Sort what is remaining by k-value.
5. Convert the base 5 primes to base 25 primes as shown above.
6. Remove k's where the base 5 project has effectively found primes for base 25.
7. Determine what k's that the base 5 project is still working on whose eventual prime would also convert to a base 25 prime.
8. Remove the k's from the determination in #7.
9. Sieve whatever k's remain for n=5K-25K (or whatever limit you wish to search).
10. In addition to your "regular" n<=5000 list of primes, please send me a list of the converted base 5 primes.
[/code]

The above is anything but an easy task. #7 is the most difficult.

I'd much rather you choose something different. If the math is not 100% clear ahead of time, this is an extremely dangerous base to get involved with. Willem was clear on the math but missed that a base 25 prime could be derived from a base 5 prime with an odd exponent.

Editor note (lol): I cannot guarantee that I have not missed something in the above. It's all that I can think of that I had to do to check Willem's work on the Riesel side.


Gary

OK I'm cancelling the Sierpinski base 25 effort, thats is just to much work to make sure is got right :smile: So now I'm only focusing on running the Sierpinski base 63 effort.

Regards

KEP

[quote=KEP;168254]OK I'm cancelling the Sierpinski base 25 effort, thats is just to much work to make sure is got right :smile: So now I'm only focusing on running the Sierpinski base 63 effort.

Regards

KEP[/quote]

Yep, it is a whole lot of effort. The Riesel side was even worse because there were k's with algebraic factors. The Sierp side should not have k's with algebraic factors because b^2+1 does not algebraically factor like b^2-1 does, i.e. (b+1)*(b-1). Fortunately Willem had a good handle on the math aspect of things and I didn't find any problem with his removal of k's that contained algebraic factors.

I do want to get it started in the next few months but I don't want to dedicate one of my quads to it. Therefore to start on it, I need to get the hard drive replaced and everything reloaded on my Window's desktop, then continue on Sierp base 31 up to n=15K (likely 3 months on 2 slower cores), and THEN I'll be able to start on Sierp base 25.

Somewhere before that time, I may run PFGW up to n=5K and see what I can do as far as removing base 5 primes that convert to base 25 primes. If we can get a correct listing of k's that need to be searched by CRUS, even at the low limit of n=5K, it won't be too bad for someone else to pick up from there.


Gary

[QUOTE=gd_barnes;168345]Yep, it is a whole lot of effort. The Riesel side was even worse because there were k's with algebraic factors. Fortunately Willem had a good handle on the math aspect of things and I didn't find any problem with his removal of k's that contained algebraic factors.

I do want to get it started in the next few months but I don't want to dedicate one of my quads to it. Therefore to start on it, I need to get the hard drive replaced and everything reloaded on my Window's desktop, then continue on Sierp base 31 up to n=15K (likely 3 months on 2 slower cores), and THEN I'll be able to start on Sierp base 25.

Somewhere before that time, I may run PFGW up to n=5K and see what I can do as far as removing base 5 primes that convert to base 25 primes. If we can get a correct listing of k's that need to be searched by CRUS, even at the low limit of n=5K, it won't be too bad for someone else to pick up from there.


Gary[/QUOTE]

Well all dependend on how I'm progressing on the Sierpinski base 63, I might take up the challenge as soon as you've started the base up. The Sierpinski base 25 is actually quite much more fun, since for the sieving sr2sieve can be used, which actually gives speed increases compared to srsieve on ~115-125%... however I would really prefer to have less than 10,000 k's remaining on sierpinski base 63 before starting up something else, especially now that I've found the perfect range-size, which doesn't requires all my memory and doesn't take to long to sieve :smile: On a foot note, I can add that in <24 hours I'll start OpenPFGW testing the n>1000-n<=5000 range for the 240133 k's remaining for Sierpinski base 63. After that I might sieve the n>5000-n<=25000 (or higher) range, all dependent on the amount of memory needed.

Now finally thanks for explaining the difficulties regarding base 25, I was not even close to get it right by myself :smile:

Take care.

Kenneth

Riesel base 22 at n=134K.
Sierp base 22 at n=121K.
Riesel base 28 at n=124K.
Sierp base 28 at n=132K.

Nothing more to report.

Whew, what a load!

Riesel Base 23
 

Riesel Base 23 (both k's) completed from n=100K to n=180K

Nothing found - Releasing

Results emailed

Base 10 (Riesel + Sierpinski) tested till n=260000.
Given the latest discoveries concerning phrot accuracy of results I will doublecheck 202769<n<260000 range using LLR before continuing.

Riesel base 22 is at n=150K.
Sierp base 22 is at n=135K.
Riesel base 28 is at n=135K.
Sierp base 28 is at n=143K.

I am extending the reservation on Riesel and Sierp base 22 to n=200K. As previously reserved, I will stop both sides of base 28 at n=150K.

I am temporarily stopping Riesel base 22 and will restart it after Sierp base 28 is complete to n=150K. Shortly I will start on the final k of Riesel base 27 for n=145K-200K.

No more primes to report on any of the bases. Only one prime so far on Sierp base 28 since n=100K.

The usual tough final few k's!

[quote=MyDogBuster;169976]Riesel Base 23 (both k's) completed from n=100K to n=180K

Nothing found - Releasing

Results emailed[/quote]


Ian,

Did you by chance sieve the file any further that you would have gotten from the CRUS reservations page? If so, could you send it to me?


Thanks,
Gary

Riesel base 22 is paused at n=150K; will start again after Riesel base 28 is complete to n=150K

Sierp base 22 is at n=144K; continuing to n=200K

Riesel base 27 is at n=170K; continuing to n=200K (currently at 2900 secs. per test; ugh!)

Riesel base 28 is at n=142K; continuing to n=150K

Sierp base 28 is complete to n=150K; now unreserved

Nothing to report.

Riesel base 22 is at n=160K; continuing to n=200K

Sierp base 22 is complete to n=150K. I changed my mind and will stop this one here. It is now unreserved.

Riesel base 27 is at n=192K; continuing to n=200K

Riesel base 28 is complete to n=150K; now unreserved.

Nothing to report.