Bases > 1030 and k's > CK

[lalera]

Originally Posted by sweety439

For k=4, k=64, and k=144:

Odd n has factor of 5
Even n has algebra factors

For k=100:

Odd n has factor of 101
Even n has algebra factors

Thus R2019 has only 6 k’s remain at n=100K:

84, 114, 204, 242, 296, 302

hi,
perl hiddenPowers.pl pl_remain.txt
4*2019^n-1 n=0 mod 2 factors due to 2^2
64*2019^n-1 n=0 mod 2 factors due to 8^2
64*2019^n-1 n=0 mod 3 factors due to 4^3
100*2019^n-1 n=0 mod 2 factors due to 10^2
144*2019^n-1 n=0 mod 2 factors due to 12^2

i see no reason to remove these k´s

[VBCurtis]

Originally Posted by lalera

hi,
perl hiddenPowers.pl pl_remain.txt
4*2019^n-1 n=0 mod 2 factors due to 2^2
64*2019^n-1 n=0 mod 2 factors due to 8^2
64*2019^n-1 n=0 mod 3 factors due to 4^3
100*2019^n-1 n=0 mod 2 factors due to 10^2
144*2019^n-1 n=0 mod 2 factors due to 12^2

i see no reason to remove these k´s

... because you don't understand sweety's post?
If every odd power has a trivial factor, and every even power factors as a difference of squares, which powers are going to generate a prime for you?

[lalera]

Originally Posted by VBCurtis

... because you don't understand sweety's post?
If every odd power has a trivial factor, and every even power factors as a difference of squares, which powers are going to generate a prime for you?

hi,

i did not understand sweety439´s post
i am not a mathematician
i thought that only if the script tells me something like
(example: 8*125^n-1 every n factors due to x^3)
i can remove the entire k

thank you for the info

[gd_barnes]

Sweety's post is correct. You can remove those k's from your search. They will never be prime. Based on your page, there really are only 6 k's remaining. You can kind of notice this when sieving if you see an unusually low number of n's remaining for a k. The fact that the k's are perfect powers and there are few n's remaining in the sieve is another clue.

You can see these types of algebraic factors shown on the Riesel page for different bases <= 1030. If the algebra and reason for removing them is not clear to you, it would be safer for you to stick with Sierpinski bases (that still have some k's with algebraic factors but are far less likely) or participate in the project for bases <= 1030. There are many bases in the recommended thread with 4 or 5 k's remaining that can be searched from n=100K to 200K or higher.

Not all versions of sr(x)sieve will remove all k's with algebraic factors.

[lalera]

Originally Posted by gd_barnes

Sweety's post is correct. You can remove those k's from your search. They will never be prime. Based on your page, there really are only 6 k's remaining. You can kind of notice this when sieving if you see an unusually low number of n's remaining for a k. The fact that the k's are perfect powers and there are few n's remaining in the sieve is another clue.

You can see these types of algebraic factors shown on the Riesel page for different bases <= 1030. If the algebra and reason for removing them is not clear to you, it would be safer for you to stick with Sierpinski bases (that still have some k's with algebraic factors but are far less likely) or participate in the project for bases <= 1030. There are many bases in the recommended thread with 4 or 5 k's remaining that can be searched from n=100K to 200K or higher.

Not all versions of sr(x)sieve will remove all k's with algebraic factors.

hi,
thank you!

[NHoodMath]

Reserving Sierp. base 2020 (all 21 k's) from 10K-20K. (At 10K the testing was progressing at about n=1K/day) also, just ask if you want the k's remaining at n=10K for this one.

Anyone want all 62 k's remaining for the Riesel side for 8K-10K?

[VBCurtis]

Originally Posted by NHoodMath

Anyone want all 62 k's remaining for the Riesel side for 8K-10K?

If you're offering a sieve file for testing, I'll be happy to run 8k-10k for you.
Email it to my forum name at gmail, prettyplease.

[NHoodMath]

Originally Posted by VBCurtis

If you're offering a sieve file for testing, I'll be happy to run 8k-10k for you.
Email it to my forum name at gmail, prettyplease.

How long does a test of a 20000 digit long number take on your computer @VBCurtis? That way I can judge optimal depth

[VBCurtis]

Just do depth optimal for your own machine; it doesn't make sense to compare your sieve time to my LLR time. Also, I'll be running the file on multiple machines, each of a different speed, so I can't honestly answer your question.

Or, sieve to whatever depth you think reasonable, and I can sieve a few more hours if I deem it useful.

[NHoodMath]

Find attached the 6915 candidate sequences for R2020 8K=10K to n=5G (102.2s/n)


Also, status update on yesterday's S2020 reservation:
Testing is at n=14676, 3 new primes found, 18 k's remain:
775*2020^10658+1
612*2020^11836+1
901*2020^14159+1

[VBCurtis]

Thanks for the file. It yielded 4 primes for 3 k's:
558*2020^8312-1
644*2020^9240-1
681*2020^9297-1
644*2020^9634-1

I haven't counted the k's to double-check your count, but you said 62 k's at 8000 so now there are 59 k's at 10,000.

I think I know how to pull them from the sieve file you gave me and set up a new sieve; if I manage that, I'll run n=10k-20k to sieve Wednesday and LLR from tomorrow night through the weekend. EDIT: unless you'd like to continue testing yourself- you started the base, so it's your prerogative to continue if you wish.
EDIT2: I fed the sequences into srsieve, and it pointed out k=9 and k=1296 have algebraic factors; I note both k's are perfect squares, which means I can delete all even n's for those k's (right?). I'll wait for a green light from NHoodMath before I start testing; if he'd like to test I can post the sieve file.