Bases 33-100 reservations/statuses/primes

[Flatlander]

Originally Posted by gd_barnes

Srsieve will display that message on any k that is any perfect power in most conditions for a Riesel form. For Sierpinski forms, they are less common. I believe that only perfect cubes and higher can contain algebraic factors on Sierpinski forms, although I haven't checked that completely. See more explanation below.

It does not mean you can remove the k's from testing. Srsieve makes that statement when there are SOME n-values remaining that can be manually eliminated because they contain algebraic factors. Notice use of the word "SOME". It doesn't mean that all n-values can be elminated; only some of them. For the k to be removed, all n-values would have to be eliminated.

Situations in which srsieve will make that statement:

1. For ANY k on ANY base that is a perfect square, when sieving, all n-values that are divisible by 2 can be manually removed.
2. For any k on any base that is a perfect cube, all n-values that are divisible by 3 can be manually removed.
3. (etc.) for k's that are perfect 5th powers, 7th powers, 11th powers, or any prime power where p=power, any n's divisible by p can be manually removed.

Taken to an extreme, for k=2048, which is 2^11, you could manually eliminate all n-values that are divisible by 11.

To put the above in a different way: You can only eliminate the k if manually removing all of these n-values leaves you with no n's remaining, which would have been the case had you attempted to sieve 900*67^n-1. Had you sieved it, you would have ended up with a sieve file with very few EVEN n-values remaining and zero ODD n-values remaining. Once you manually removed the n's divisible by 2, you would have had nothing left. That means that the k-value can be removed from conjecture testing because it has partial algebraic factors that combine with a numeric factor to make a full "covering set" of factors.

Analysis on both k=125 and 729 shows that they should remain because there is no factor or factors that eliminate the n's that the algebraic factors do not. Sorry; you can't get away with removing them this time! lol

When sieving, as per the above, on k=125, you can manually remove all n-values divisible by 3. On k=729, that is one of the few that you can eliminate n-values that are divisible by 2 -or- that are divisible by 3. In effect, you're only left with n-values that are n==(1 or 5 mod 6). If you manually remove those n's, you'll stop getting that message from srsieve.

k=729 would normally be extremely low weight except for the fact that it is divisible by 3, which eliminates any possibility of a factor of 3 for all n-values. That increases the weight to something like a k that is a perfect square.

A k-value that would be extremely low-weight is one that is a perfect square and cube but is not divisible by 2, 3, or 5. I think the lowest one of that nature would be 7^6=117649, which would only be an issue on very few bases.


Gary

Was that a 'yes' or a 'no'? lol
Only kidding. It'll make sense when I'm not tired. (Possibly.)

Riesel base 70 tested to 25k. Unreserving.

Primes >5K:
2621*70^6247-1
5925*70^8850-1
2699*70^15455-1

Ks remaining:
729*70^n-1
1776*70^n-1
2202*70^n-1
5468*70^n-1

Tested with WinPFGW so no results.out file.

btw When I mentioned k = 125 I was refering to 125*2^n-1 I tested for RPS.

[gd_barnes]

Originally Posted by Flatlander

Was that a 'yes' or a 'no'? lol
Only kidding. It'll make sense when I'm not tired. (Possibly.)

Riesel base 70 tested to 25k. Unreserving.

Primes >5K:
2621*70^6247-1
5925*70^8850-1
2699*70^15455-1

Ks remaining:
729*70^n-1
1776*70^n-1
2202*70^n-1
5468*70^n-1

Tested with WinPFGW so no results.out file.

btw When I mentioned k = 125 I was refering to 125*2^n-1 I tested for RPS.

Riesel bases 67 and 70 would be excellent bases to make team efforts out of. They're proof is just challenging enough to make them interesting but not so challenging that they'll die out. I'd expect a final prime on them in the n=100K-500K range somewhere barring some very good or bad luck on them...still very large but not ridiculous.

We won't do more team drives right now but they are definite possibilities for the future.


Gary

[KEP]

Reserving Sierpinski base 63 Can anyone tell me which k's can be excluded from testing beyond n=1000?

Here is how I'm going to do it:

1. Strict test all k<=37565866 up to n=1000 (already in progress)
2. Remove the k's that can be excluded before sieving
3. Sieve all remaining candidates for n>1000 to n<=25000
4. PRP test all candidate-pairs to n=25000
5. Verify the PRPs
6. Send primes for n>1000 aswell remaining k's to Gary

I know this sounds like a big task, but as soon as my base 3 reservations clear up, I'm gonna put all six availeable cores on the task.

Regards

KEP

[MyDogBuster]

Riesel Base 45

4484*45^16012-1 is prime! (186.3988s+0.0016s)

Only 21k's remaining

Started that k and found the prime on test 156, about 2 hours worth.

[gd_barnes]

Originally Posted by MyDogBuster

Riesel Base 45

4484*45^16012-1 is prime! (186.3988s+0.0016s)

Only 21k's remaining

Started that k and found the prime on test 156, about 2 hours worth.

I show that there are 20 k's remaining since you've eliminated 2 of them now.

One question: You said you were testing each k individually up to n=100K. Have you already tested several of them to n=100K? If so, I'll show that on the pages.


Gary

[gd_barnes]

Originally Posted by KEP

Reserving Sierpinski base 63 Can anyone tell me which k's can be excluded from testing beyond n=1000?

Here is how I'm going to do it:

1. Strict test all k<=37565866 up to n=1000 (already in progress)
2. Remove the k's that can be excluded before sieving
3. Sieve all remaining candidates for n>1000 to n<=25000
4. PRP test all candidate-pairs to n=25000
5. Verify the PRPs
6. Send primes for n>1000 aswell remaining k's to Gary

I know this sounds like a big task, but as soon as my base 3 reservations clear up, I'm gonna put all six availeable cores on the task.

Regards

KEP

Well, I can say that you like the really BIG and TOUGH efforts Kenneth! lol I noticed that you really like the bases that are 2^q-1, which of course are some of the biggest conjectures because they are usually the most prime bases. Your plan of action sounds very good.

You do realize that this is likely 2-5 CPU years worth of work, correct? Regardless, no problem. If you end up testing it to n=10K or 15K and leaving some sieved files behind for us, that's OK. If you're able to get all the way to n=25K (I definitely could not! ), then I would congradulate you on a job very well done!

Exclusions:
1. Odd k's due to a trivial factor of 2.
2. k==(30 mod 31) due to a trivial factor of 31.
3. k's that are multiples of the base where k+1 is not prime.

On odd Sierp bases, GFNs have a trivial factor of 2 so are not an issue.

On #3, I'll give some examples:

k=62, 124, 186, and 248 would be excluded from testing because 63, 125, 187, and 249 are not prime.

k=310 and 372 would be INcluded in testing because 311 and 373 are prime.

The exclusions for multiples of the base are the same on all bases. Check for k-1 being prime on the Riesel side and check for k+1 being prime on the Sierp side. If it's prime, include it; if it's not prime, exclude it.


Gary

[MyDogBuster]

Riesel Base 45

6372*45^23067-1 is prime! (327.8198s+0.0024s)

19 left

One question: You said you were testing each k individually up to n=100K. Have you already tested several of them to n=100K? If so, I'll show that on the pages.

The following k's are tested up to n=100K:

372, 1312, 15432

Do you need the results files on this stuff? Primes & non-primes?

[MyDogBuster]

Riesel Base 45

20654*45^18103-1 is prime! (217.9591s+0.0017s)

18 Left

[gd_barnes]

Originally Posted by MyDogBuster

Do you need the results files on this stuff? Primes & non-primes?

Yes on both but to avoid inundating me with Emails, you can send them all when you are done. However you want is fine but I'd prefer more than one k per Email. lol

BTW, one reason that I asked if you could post the k's that you had tested to n=100K is that I can now unreserve just those k's for you since you said that was your testing limit. Technically others can now take them higher. That's the good thing about searching by k-value!

If you now think you'd like to continue above n=100K on the k's without a prime, let me know and I'll re-reserve them.


Gary

[henryzz]

i have now taken riesel base 94 to 51k with no primes
unreserving

[gd_barnes]

Originally Posted by henryzz

i have now taken riesel base 94 to 51k with no primes
unreserving

Can you post a results file? Thanks.


Gary