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-   -   Bases 2 & 4 reservations/statuses/primes (https://www.mersenneforum.org/showthread.php?t=9830)

Jean Penné 2007-12-19 13:31

Bases 2 & 4 reservations/statuses/primes
 
Hello Gary,

Congrats for organizing this search!
I am working alone on the Riesel base 4 candidates for a while, so I wish to reserve all the divisible by 3 k's candidates, up to n = 131072 base 4 for now...

The remaining k's I wish to reserve are :

9519, 13854, 14361, 16734, 19401 and 20049, which are marked as available on your reservation page. I already eliminated all the others...

Regards,
Jean

gd_barnes 2007-12-19 14:34

[quote=Jean Penné;121063]Hello Gary,

Congrats for organizing this search!
I am working alone on the Riesel base 4 candidates for a while, so I wish to reserve all the divisible by 3 k's candidates, up to n = 131072 base 4 for now...

The remaining k's I wish to reserve are :

9519, 13854, 14361, 16734, 19401 and 20049, which are marked as available on your reservation page. I already eliminated all the others...

Regards,
Jean[/quote]


Hi Jean,

Thank you and welcome to the effort! It's nice to have you on board. The k's are available and I will show them reserved by you today. It looks like you're now the official base 4 person; both Riesel and Sierpinski! :smile:

If you have the time, come vote in our poll in the lounge [URL="http://www.mersenneforum.org/showthread.php?t=9764"]here[/URL].


Gary

tcadigan 2007-12-20 03:32

[QUOTE=gd_barnes;121069]Hi Jean,
...
It looks like you're now the official base 4 person; both Riesel and Sierpinski! :smile:
...


Gary[/QUOTE]

I'm still around on the Sierpinski side of things....granted I'm really slow...but I'm still around. people are free to reserve any range they want but since no one has stepped forward I keep slowly going forward with it...

64494 is at 1770506 and still no prime

gd_barnes 2007-12-20 03:54

[quote=tcadigan;121102]I'm still around on the Sierpinski side of things....granted I'm really slow...but I'm still around. people are free to reserve any range they want but since no one has stepped forward I keep slowly going forward with it...

64494 is at 1770506 and still no prime[/quote]


Thanks for the update Tcadigan. I'll put you down for testing completion of n=885.2K base 4. I had previously noticed that you were searching one k for Sierp base 4 so sorry about the omission there.

If you'd like to pick up a smaller search effort that also LLR's as fast as base 2, we've got 55 k's for Sierp base 16, all tested to just n=25K that are ready for testing. At some future time, we also want to start on Riesel base 16 from the beginning.


Thanks,
Gary

gd_barnes 2008-01-08 06:27

Riesel/Sierp base 2/4 reservations/statuses/primes
 
[quote=Jean Penné;122412]

About the second question, when the base is a power of two, there may be MOB k values which are also power of two, and then the candidates are not only Generalized Fermat Numbers, but very Fermat Numbers, so, I think these k's should be excluded (It is conjectured that there are a finite number of Fermat primes, and most of the mathematicians believe that F4 = 65537 is the largest one...).
As I remarked in another thread, proving that F4 is the largest Fermat prime is equivalent to proving that 65536 is an even Sierpinski number...
But, if so, the covering set would be infinite, because it is well known that Fermat numbers are pairwise coprime...

Regards,
Jean[/quote]

(Edit note: MOB = multiples of base)

Robert, Citrix, Axn, Geoff, Masser, or other people with intimate knowledge of the math's behind the conjectures, here is what I would propose (if it has not been proposed already) that Jean agrees with:

In order to prove the Sierpinski conjecture for any base, all Generalized Fermat #'s as well as very Fermat #'s, i.e. any form that reduces to 2^n+1, should be excluded from those conjectures.

In a nutshell, here is what I'm working towards as determining the Riesel/Sierpinski conjecture proofs on the "Conjectures 'R Us" web pages:


1. All generalized Fermat #'s (18*18^n+1) and very Fermat #'s (65536*4^n+1 or 65536*16^n+1) will be excluded from the conjectures.

2. Any k that obtains a full covering set in any manner from ALGEBRAIC factors will be excluded. In many instances, this includes k's where there is a partial covering set of numeric factors (or a single numeric factor) and a partial covering set of algebraic factors that combine to make a full covering set.

3. All k below the lowest k found to have a NUMERIC covering set must have a prime including multiples of the base (MOB) but excluding the conditions in #1 and #2 above. I will add MOB and exclude GFn's in the near future on the pages. There are very few MOB if GFNs are excluded.

4. All n must be >= 1.


All input and opinions are welcome.

Citrix, if you think this is misplaced, feel free to move it around somewhere.


Thanks,
Gary

Jean Penné 2008-01-08 20:33

Liskovets-Gallot numbers are beautiful for us!
 
Hi,

On the 23 May 2006, Citrix warned us, in the Sierpinski base 4 thread, about this problem :

[URL]http://www.primepuzzles.net/problems/prob_036.htm[/URL]

To be short, the Liskovets assertion is :

There are some k values such that k*2^n+1 is composite for all n values of certain fixed parity, and some k values such that k*2^n-1 is composite for all n values of certain fixed parity.

It is almost evident that these k values must be searched only amongst the multiples of 3 (the assertion is trivial if 3 does not divide k) :

If k == 1 mod 3, then 3 | k*2^n-1 if n is even, and 3 | k*2^n+1 if n is odd.
If k == 2 mod 3, then 3 | k*2^n+1 if n is even, and 3 | k*2^n-1 if n is odd.

Almost immediately after, Yves Gallot discovered the first four Liskovets-Gallot numbers ever produced :

k*2^n+1=composite for all n=even: k=66741
k*2^n+1=composite for all n=odd: k=95283
k*2^n-1=composite for all n=even: k=39939
k*2^n-1=composite for all n=odd: k=172677

And Yves said that "I conjecture that 66741, 95283, 39939, ... and 172677 are the smallest solutions for the forms - having no algebraic factorization (such as 4*2^n-1 or 9*2^-1) - but I can't prove it."

For several reasons, I think it would be interesting for us to coordinate the search in order to prove these four conjectures :

1) They involve only k values that are multiples of 3, so the success will no more be depending of the SoB or Rieselsieve one.

2) For the n even Sierpinski case, only k = 23451 and k = 60849 are remaining, with n up to more than 1,900,000 that is to say there are only two big primes to found, then the conjecture is proven!

3) For the n even Riesel (third line above) there are only four k values remaining : 9519, 14361, 19401 and 20049, although the search is only at the beginning!

4) For the two remaining n odd Sierpinski / Riesel (which can be tranlated as
base 4, k even, and doubling the Gallot values : 190566 for k*4^n+1, 345354 for k*4^n-1) I began to explore the problem, by eliminating all k's yielding a prime for n < 4096, eliminating the perfect square k values for Riesel, eliminating the MOB that are redondant, etc...

Finally, there were 42 k values remaining for +1, 114 for -1, and after sieving rapidly with NewPGen, and LLRing up to ~32K, I have now 21 values remaining for +1 and 37 values for -1.

I would be happy to know your opinion about all that...
Regards,
Jean

gd_barnes 2008-01-10 19:15

[quote=Jean Penné;122480]Hi,

On the 23 May 2006, Citrix warned us, in the Sierpinski base 4 thread, about this problem :

[URL]http://www.primepuzzles.net/problems/prob_036.htm[/URL]

To be short, the Liskovets assertion is :

There are some k values such that k*2^n+1 is composite for all n values of certain fixed parity, and some k values such that k*2^n-1 is composite for all n values of certain fixed parity.

It is almost evident that these k values must be searched only amongst the multiples of 3 (the assertion is trivial if 3 does not divide k) :

If k == 1 mod 3, then 3 | k*2^n-1 if n is even, and 3 | k*2^n+1 if n is odd.
If k == 2 mod 3, then 3 | k*2^n+1 if n is even, and 3 | k*2^n-1 if n is odd.

Almost immediately after, Yves Gallot discovered the firt four Liskovets-Gallot numbers ever produced :

k*2^n+1=composite for all n=even: k=66741
k*2^n+1=composite for all n=odd: k=95283
k*2^n-1=composite for all n=even: k=39939
k*2^n-1=composite for all n=odd: k=172677

And Yves said that "I conjecture that 66741, 95283, 39939, ... and 172677 are the smallest solutions for the forms - having no algebraic factorization (such as 4*2^n-1 or 9*2^-1) - but I can't prove it."

For several reasons, I think it would be interesting for us to coordinate the search in order to prove these four conjectures :

1) They involve only k values that are multiples of 3, so the success will no more be depending of the SoB or Rieselsieve one.

2) For the n even Sierpinski case, only k = 23451 and k = 60849 are remaining, with n up to more than 1,900,000 that is to say there are only two big primes to found, then the conjecture is proven!

3) For the n even Riesel (third line above) there are only four k values remaining : 9519, 14361, 19401 and 20049, although the search is only at the beginning!

4) For the two remaining n odd Sierpinski / Riesel (which can be tranlated as
base 4, k even, and doubling the Gallot values : 190566 for k*4^n+1, 345354 for k*4^n-1) I began to explore the problem, by eliminating all k's yielding a prime for n < 4096, eliminating the perfect square k values for Riesel, eliminating the MOB that are redondant, etc...

Finally, there were 42 k values remaining for +1, 114 for -1, and after sieving rapidly with NewPGen, and LLRing up to ~32K, I have now 21 values remaining for +1 and 37 values for -1.

I would be happy to know your opinion about all that...
Regards,
Jean[/quote]


I responded in the "Conjecture 'R Us" thread to this.


Gary

Jean Penné 2008-01-10 19:29

[QUOTE=kar_bon;122578]i read about your post but no time yet to work with.
it's quite an interesting conjecture to prove and i'm interested in the Riesel odd/even side of this problem. it's worth another extra data page for the RPS site.
will do this for the Riesel power-2 bases for CRUS too next time.
i think i take some searching on 9519, 14361, 19401 and 20049. which ranges you searched yet? any findings?
karsten[/QUOTE]

For now, my progress on these k's follows (exponents n are in base 2) :

k = 9519 is up to n = 427816, no prime.
k = 14361 is up to n = 318510, no prime.
k = 19401 is up to n = 262578, no prime.
k = 20049 is up to n = 265144, no prime.

I thought to test these k's up to 524288 base 2 if no prime found below...
However, to day, only 9519 is running... If you have more available computing power, you may continue on the last three k's, but if so, let me know about your progress.

Regards,
Jean

gd_barnes 2008-01-10 21:42

[quote=Jean Penné;122583]For now, my progress on these k's follows (exponents n are in base 2) :

k = 9519 is up to n = 427816, no prime.
k = 14361 is up to n = 318510, no prime.
k = 19401 is up to n = 262578, no prime.
k = 20049 is up to n = 265144, no prime.

I thought to test these k's up to 524288 base 2 if no prime found below...
However, to day, only 9519 is running... If you have more available computing power, you may continue on the last three k's, but if so, let me know about your progress.

Regards,
Jean[/quote]

OK, I will make note of the test limits and unreserve k=13854, 16734, and 19464. Note that the last one is currently only on the base 16 page because it's a MOB base 4.

Here is what I show for the test limits for the k's that you're unreserving:

k=13854 and 16734; I show no work so they are still at n=100K base 4.
k=19464 per your status report of 1/7/08 is at n=137112 base 2.

Is that correct?

I'll coordinate getting the 3 unreserved k's tested. If they aren't reserved in the new few days, I'll reserve and test them.

Since you did some testing on k=19464, do you have a sieve file for that one or for any of the k's? If so, I will post them on the website.


Gary

kar_bon 2008-01-10 21:54

got sieve-files from jean for 14361, 19401 and 20049 and sieving further!

gd_barnes 2008-01-10 23:21

[quote=kar_bon;122591]got sieve-files from jean for 14361, 19401 and 20049 and sieving further![/quote]

I messed up originally here by not following the entire thread. I'll straighten out the reservations shortly. Sorry about my confusion.

You can ignore my last post.

Edit: It's all correct now. You might check the Riesel base 4 and base 16 reservations to make sure I have it correct.


Gary

Jean Penné 2008-01-11 07:38

[QUOTE=gd_barnes;122588]OK, I will make note of the test limits and unreserve k=13854, 16734, and 19464. Note that the last one is currently only on the base 16 page because it's a MOB base 4.

Here is what I show for the test limits for the k's that you're unreserving:

k=13854 and 16734; I show no work so they are still at n=100K base 4.
k=19464 per your status report of 1/7/08 is at n=137112 base 2.

Is that correct?

I'll coordinate getting the 3 unreserved k's tested. If they aren't reserved in the new few days, I'll reserve and test them.

Since you did some testing on k=19464, do you have a sieve file for that one or for any of the k's? If so, I will post them on the website.


Gary[/QUOTE]


OK for unreserving k=13854 and 16734 ; I am presently sieving for k = 19464, and I wish still test it at least up to 524288 base 2 when sieved enough...

Regards,
Jean

gd_barnes 2008-01-11 07:43

[quote=Jean Penné;122607]OK for unreserving k=13854 and 16734 ; I am presently sieving for k = 19464, and I wish still test it at least up to 524288 base 2 when sieved enough...

Regards,
Jean[/quote]


OK, are k=13854 and 16734 still at n=100K base 4?


Gary

Jean Penné 2008-01-11 08:49

[QUOTE=gd_barnes;122608]OK, are k=13854 and 16734 still at n=100K base 4?


Gary[/QUOTE]

k = 13854 is at n = 261944 base 2 (so, 128K base 4).

I did'nt worked yet on k = 16734.

Jean

Citrix 2008-01-13 04:21

Jean,

I looked at the parity thing you mentioned. It sounds interesting, perhaps we can go to higher bases once we are done with 256.

I also looked at all k's 1-32, that are supper fast for all possible parities up to 2^100. There were some really low weight sequences and some high weight sequences. Do you think we might have similar luck like RPS or 15K with some of these high weight or low weight sequences and possibly find a 10M prime?

What do you think? If you or any one else is interested please let me know.

Thanks:smile:

Citrix 2008-01-13 05:08

Low weight Reisel
K=29 not included as it is already low weight.
[code]
k*2^m*(2^i)^n-1 // last column is the candidates left, approx estimate of weight
19 9 17 163
19 9 34 332
15 8 35 244
15 28 35 243
19 9 51 496
21 15 55 480
19 2 63 549
21 45 65 416
23 39 65 554
19 43 68 664
21 47 69 613
27 15 69 623
15 1 70 456
15 7 70 384
15 15 70 481
15 21 70 453
15 29 70 483
15 35 70 483
15 43 70 482
15 49 70 483
15 57 70 388
15 63 70 485
15 31 74 457
[/code]

Jean Penné 2008-01-13 07:26

[QUOTE=Citrix;122746]Jean,

I looked at the parity thing you mentioned. It sounds interesting, perhaps we can go to higher bases once we are done with 256.

I also looked at all k's 1-32, that are supper fast for all possible parities up to 2^100. There were some really low weight sequences and some high weight sequences. Do you think we might have similar luck like RPS or 15K with some of these high weight or low weight sequences and possibly find a 10M prime?

What do you think? If you or any one else is interested please let me know.

Thanks:smile:[/QUOTE]

Harsh,

Presently, I am more interested in trying to prove one or more of these four mathematical conjectures, than to find large primes (although it may be a subproduct).
Moreover, I hope we will not need to find a 10M prime before proving at least one of them!
So, perhaps it would be better to restrict this project to base 4 for now, and not to dissipate our efforts too much...
But, indeed there is place for other similar projects!

Regards,
Jean

gd_barnes 2008-01-14 19:19

[quote=Jean Penné;122480]Hi,

On the 23 May 2006, Citrix warned us, in the Sierpinski base 4 thread, about this problem :

[URL]http://www.primepuzzles.net/problems/prob_036.htm[/URL]

To be short, the Liskovets assertion is :

There are some k values such that k*2^n+1 is composite for all n values of certain fixed parity, and some k values such that k*2^n-1 is composite for all n values of certain fixed parity.

It is almost evident that these k values must be searched only amongst the multiples of 3 (the assertion is trivial if 3 does not divide k) :

If k == 1 mod 3, then 3 | k*2^n-1 if n is even, and 3 | k*2^n+1 if n is odd.
If k == 2 mod 3, then 3 | k*2^n+1 if n is even, and 3 | k*2^n-1 if n is odd.

Almost immediately after, Yves Gallot discovered the firt four Liskovets-Gallot numbers ever produced :

k*2^n+1=composite for all n=even: k=66741
k*2^n+1=composite for all n=odd: k=95283
k*2^n-1=composite for all n=even: k=39939
k*2^n-1=composite for all n=odd: k=172677

And Yves said that "I conjecture that 66741, 95283, 39939, ... and 172677 are the smallest solutions for the forms - having no algebraic factorization (such as 4*2^n-1 or 9*2^-1) - but I can't prove it."

For several reasons, I think it would be interesting for us to coordinate the search in order to prove these four conjectures :

1) They involve only k values that are multiples of 3, so the success will no more be depending of the SoB or Rieselsieve one.

2) For the n even Sierpinski case, only k = 23451 and k = 60849 are remaining, with n up to more than 1,900,000 that is to say there are only two big primes to found, then the conjecture is proven!

3) For the n even Riesel (third line above) there are only four k values remaining : 9519, 14361, 19401 and 20049, although the search is only at the beginning!

4) For the two remaining n odd Sierpinski / Riesel (which can be tranlated as
base 4, k even, and doubling the Gallot values : 190566 for k*4^n+1, 345354 for k*4^n-1) I began to explore the problem, by eliminating all k's yielding a prime for n < 4096, eliminating the perfect square k values for Riesel, eliminating the MOB that are redondant, etc...

Finally, there were 42 k values remaining for +1, 114 for -1, and after sieving rapidly with NewPGen, and LLRing up to ~32K, I have now 21 values remaining for +1 and 37 values for -1.

I would be happy to know your opinion about all that...
Regards,
Jean[/quote]


Jean,

Is there any reason that we are not testing even k's (i.e. multiples of the base) with these conjectures? If a k is even but is not divisible by 4, it yields a different set of factors and prime than any other odd k.

I am testing the Sierp odd-n conjecture of k=95283. Can you tell me how you arrived at 21 k-values remaining at n=32K? I have now tested up to n=56K. I just now finished sieving up to n=200K and am starting LLRing now.

At n=56K, I show 22 odd k's and 8 even k's remaining that are not redundant with other k's remaining; for a total of 30 k's.

At n=32K, I showed 26 odd k's and 9 even k's remaining; for a total of 35 k's.

I checked the top-5000 site for previous smaller primes and there were none for these k's so I wonder why you have less k's remaining than me.

Here are the k's that I show remaining at n=32K, both odd and even, and primes that I found for n=32K-56K for the Sierp odd-n conjecture:

[code]
k comments/prime
2943
9267
17937 prime n=53927
24693
26613
29322 even
32247
35787 prime n=36639
37953
38463
39297
43398 even
46623
46902 even
47598 even
50433
53133
60357
60963
61137
61158 even; prime n=48593
62307 prime n=44559
67542 even
67758 even
70467
75183 prime n=35481
78753
80463
83418 even
84363
85287
85434 even
91437
93477
93663
[/code]


Thanks,
Gary

Jean Penné 2008-01-14 21:17

[QUOTE=gd_barnes;122833]Jean,

Is there any reason that we are not testing even k's (i.e. multiples of the base) with these conjectures? If a k is even but is not divisible by 4, it yields a different set of factors and prime than any other odd k.

I am testing the Sierp odd-n conjecture of k=95283. Can you tell me how you arrived at 21 k-values remaining at n=32K? I have now tested up to n=56K. I just now finished sieving up to n=200K and am starting LLRing now.

At n=56K, I show 22 odd k's and 8 even k's remaining that are not redundant with other k's remaining; for a total of 30 k's.

At n=32K, I showed 26 odd k's and 9 even k's remaining; for a total of 35 k's.

I checked the top-5000 site for previous smaller primes and there were none for these k's so I wonder why you have less k's remaining than me.

Here are the k's that I show remaining at n=32K, both odd and even, and primes that I found for n=32K-56K for the Sierp odd-n conjecture:

[code]
k comments/prime
2943
9267
17937 prime n=53927
24693
26613
29322 even
32247
35787 prime n=36639
37953
38463
39297
43398 even
46623
46902 even
47598 even
50433
53133
60357
60963
61137
61158 even; prime n=48593
62307 prime n=44559
67542 even
67758 even
70467
75183 prime n=35481
78753
80463
83418 even
84363
85287
85434 even
91437
93477
93663
[/code]


Thanks,
Gary[/QUOTE]

In the definitions of these four conjectures, the k multipliers must be odd!
For example : 46902*2^n+1 is the same as 23451*2^(n+1)=+1 and if n is odd, n+1 is even, so, you are testing an even exponents candidate!
So, the 8 even k's remaining are relevant to the even n conjecture, and not to the odd n one...

Also, I tested k = 46623 up to n = 79553 and found a prime, so me are almost matching now... I am terminating to gather my results, and will send them to this thread as soon as possible.
Regards,
Jean

gd_barnes 2008-01-14 22:42

[quote=Jean Penné;122841]In the definitions of these four conjectures, the k multipliers must be odd!
For example : 46902*2^n+1 is the same as 23451*2^(n+1)=+1 and if n is odd, n+1 is even, so, you are testing an even exponents candidate!
So, the 8 even k's remaining are relevant to the even n conjecture, and not to the odd n one...

Also, I tested k = 46623 up to n = 79553 and found a prime, so me are almost matching now... I am terminating to gather my results, and will send them to this thread as soon as possible.
Regards,
Jean[/quote]

Well, DUH!! :blush: I will remove the even k's that obviously go with the even-n conjecture from my LLRing. :rolleyes:


Gary

gd_barnes 2008-01-15 18:37

I have now run the Sierp odd-n conjectures up to n=115K and will be continuing on to n=200K sometime next week after completing some sieving for conjectures team drive #1 and a couple of other things. Below are the k's left at n=32K with primes found for n=32K-115K.

I decided to leave the even k's in because in effect it is testing the even conjecture for all k < 95282/2=47641 and I had already sieved them. That should save a lot of effort on that side.

[code]
k comments/prime
2943 prime n=108041
9267
17937 prime n=53927
24693
26613 prime n=89749
29322 even; prime n=91367
32247
35787 prime n=36639
37953
38463 prime n=58753
39297
43398 even; prime n=72873
46623 prime n=79553
46902 even
47598 even; prime n=105899
50433
53133
60357
60963 prime n=73409
61137
61158 even; prime n=48593
62307 prime n=44559
67542 even
67758 even
70467
75183 prime n=35481
78753 prime n=63761
80463
83418 even; prime n=80593
84363
85287
85434 even
91437
93477 prime n=63251
93663 prime n=82317
[/code]


Total of 14 odd k's and 4 even k's remaining.

So...based on this effort by itself, here are the statuses of the base 2 Sierp odd-n and even-n cojectures:

Odd-n:
14 k's remaining at n=115K from odd k's above. k's remaining:
9267
24693
32247
37953
39297
50433
53133
60357
61137
70467
80463
84363
85287
91437


Even-n:
47641<k<66741: still needs to be tested.
k<=47641: 4 k's remaining at n=115K from even k's above. k's remaining converted to odd-k:
23451
33771
33879
42717

Edit: I just now realized that it was already stated that only k=23451 and 60849 are remaining on the even-n side as a result of the Sierp base 4 project. OK, NEXT time I'll remove the even k's from my testing. Ergh!


Gary

Jean Penné 2008-01-15 20:28

Gathered results for k*2^n+1, n odd
 
Gary,

I am gathering my results about the four conjectures, which requires a lot of work...
So, we will be able to compare with your results!

Here for +1 and n odd : There are 23 remaining candidates, and 42 primes found.

1) Remaining :

[CODE] k 2k tested up to (n-1 base 2)

9267 18534 1967862
32247 64494 1770506
37953 75906 33448
38463 76926 34320
39297 78594 35166
50433 100866 46076
53133 106266 87428
56643 113286 33348
60357 120714 46166
60963 121926 32912
61137 122274 33150
62307 124614 35342
70467 140934 46358
75183 150366 32840
78153 156306 32976
78483 156966 33096
78753 157506 55640
80463 160926 35660
84363 168726 35008
85287 170574 33106
91437 182874 33034
93477 186954 34846
93663 187326 67844
[/CODE]

2) Primes :

[CODE]Normalized As discovered
k n
93 20917 186*2^20916+1 is prime! Time: 786.013 ms.
2943 108041 5886*2^108040+1 is prime! by Jean Penné 06/02/05, 09:28AM
5193 4277 10386*2^4276+1 is prime! Time: 59.124 ms.
5703 5149 11406*2^5148+1 is prime! Time: 99.286 ms.
5823 8105 11646*2^8104+1 is prime! Time: 384.321 ms.
6807 4415 13614*2^4414+1 is prime! Time: 64.834 ms.
6843 14753 13686*2^14752+1 is prime! Time: 935.778 ms.
7233 4277 14466*2^4276+1 is prime! Time: 58.406 ms.
9777 18975 19554*2^18974+1 is prime! Time: 791.931 ms.
10923 6801 21846*2^6800+1 is prime! Time: 177.623 ms.
14397 4347 28794*2^4346+1 is prime! Time: 59.056 ms.
16917 12799 33834*2^12798+1 is prime! Time: 829.050 ms.
17457 29563 34914*2^29562+1 is prime! by tcadigan 28/01/05, 07:13AM
17937 53927 35874*2^53926+1 is prime! by tcadigan 28/01/05, 06:41AM
20997 8191 41994*2^8190+1 is prime! Time: 384.323 ms.
22653 28969 45306*2^28968+1 is prime! by Mark 27/01/05, 11:29PM
24693 357417 49386*2^357416+1 is Prime! by Footmaster 25/05/05, 08:44AM
25083 24981 50166*2^24980+1 is prime! by Mark 27/01/05, 11:29PM
25917 9671 51834*2^9670+1 is prime! Time: 447.572 ms.
26613 89749 53226*2^89748+1 is prime! Time: 25.000 sec.
30933 4433 61866*2^4432+1 is prime! Time: 59.831 ms.
35787 36639 71574*2^36638+1 is prime! Time: 6.016 sec.
40857 5383 81714*2^5382+1 is prime! Time: 154.925 ms.
42993 16165 85986*2^16164+1 is prime! Time: 1.223 sec.
43167 9795 86334*2^9794+1 is prime! Time: 403.492 ms.
46623 79553 93246*2^79552+1 is prime! Time: 28.184 sec.
49563 5813 99126*2^5812+1 is prime! Time: 186.733 ms.
60273 7421 120546*2^7420+1 is prime! Time: 218.279 ms.
63357 4211 126714*2^4210+1 is prime! Time: 136.667 ms.
65223 4189 130446*2^4188+1 is prime! Time: 136.782 ms.
65253 10301 130506*2^10300+1 is prime! Time: 427.195 ms.
67917 13079 135834*2^13078+1 is prime! Time: 644.241 ms.
69963 5205 139926*2^5204+1 is prime! Time: 152.156 ms.
72537 15771 145074*2^15770+1 is prime! Time: 1.199 sec.
73023 17965 146046*2^17964+1 is prime! Time: 1.349 sec.
78543 10089 157086*2^10088+1 is prime! Time: 419.114 ms.
80517 5423 161034*2^5422+1 is prime! Time: 154.232 ms.
81147 17615 162294*2^17614+1 is prime! Time: 1.331 sec.
82197 5079 164394*2^5078+1 is prime! Time: 149.421 ms.
88863 9825 177726*2^9824+1 is prime! Time: 405.011 ms.
91383 15333 182766*2^15332+1 is prime! Time: 1.173 sec.
93033 30473 186066*2^30472+1 is prime! Time: 5.037 sec.
[/CODE]

Note : The name of the discoverer is shown only for primes found by the Sierpinski base 4 project.

Regards,
Jean

gd_barnes 2008-01-15 21:39

For the Sierp odd-n conjecture, here's an update of both lists with the primes that I found and the Sierp base 4 primes with even k's removed from my list. There was only 1 Sierp base 4 prime not on my list. I ended up testing up to n=118K on all k's before stopping.

I was a little confused as to why you have three k's on your list that have a prime at n=1.

This balancing should make things much easier.

Your list with my primes and test limits:
[code]
tested to
k 2k (n-1 base 2) prime
9267 18534 1967862
32247 64494 1770506
37953 75906 118K
38463 76926 58753
39297 78594 118K
50433 100866 118K
53133 106266 118K
56643 113286 1 (??) 56643*2^1+1 is prime!
60357 120714 118K
60963 121926 73409
61137 122274 118K
62307 124614 44559
70467 140934 118K
75183 150366 35481
78153 156306 1 (??) 78153*2^1+1 is prime!
78483 156966 1 (??) 78483*2^1+1 is prime!
78753 157506 63761
80463 160926 118K
84363 168726 118K
85287 170574 118K
91437 182874 118K
93477 186954 63251
93663 187326 82317
[/code]


My list with Sierp base 4 primes and test limits and removal of even k's:
[code]
k prime test limit comments
2943 108041
9267 1.97M Sierp base 4
17937 53927
24693 357417 Sierp base 4
26613 89749
32247 1.77M Sierp base 4
35787 36639
37953 118K
38463 58753
39297 118K
46623 79553
50433 118K
53133 118K
60357 118K
60963 73409
61137 118K
62307 44559
70467 118K
75183 35481
78753 63761
80463 118K
84363 118K
85287 118K
91437 118K
93477 63251
93663 82317
[/code]


The bottom line as now shown on both lists is that we have 13 k's remaining, 11 of which have been tested to n=118K and the other 2 of which have been tested very high with Sierp base 4. This balances with the 14 odd k's that I said I had remaining previously minus the one removed from Sierp base 4.


Gary

Jean Penné 2008-01-16 08:13

[QUOTE=gd_barnes;122911]For the Sierp odd-n conjecture, here's an update of both lists with the primes that I found and the Sierp base 4 primes with even k's removed from my list. There was only 1 Sierp base 4 prime not on my list. I ended up testing up to n=118K on all k's before stopping.

I was a little confused as to why you have three k's on your list that have a prime at n=1.

This balancing should make things much easier.

Your list with my primes and test limits:
[code]
tested to
k 2k (n-1 base 2) prime
9267 18534 1967862
32247 64494 1770506
37953 75906 118K
38463 76926 58753
39297 78594 118K
50433 100866 118K
53133 106266 118K
56643 113286 1 (??) 56643*2^1+1 is prime!
60357 120714 118K
60963 121926 73409
61137 122274 118K
62307 124614 44559
70467 140934 118K
75183 150366 35481
78153 156306 1 (??) 78153*2^1+1 is prime!
78483 156966 1 (??) 78483*2^1+1 is prime!
78753 157506 63761
80463 160926 118K
84363 168726 118K
85287 170574 118K
91437 182874 118K
93477 186954 63251
93663 187326 82317
[/code]


My list with Sierp base 4 primes and test limits and removal of even k's:
[code]
k prime test limit comments
2943 108041
9267 1.97M Sierp base 4
17937 53927
24693 357417 Sierp base 4
26613 89749
32247 1.77M Sierp base 4
35787 36639
37953 118K
38463 58753
39297 118K
46623 79553
50433 118K
53133 118K
60357 118K
60963 73409
61137 118K
62307 44559
70467 118K
75183 35481
78753 63761
80463 118K
84363 118K
85287 118K
91437 118K
93477 63251
93663 82317
[/code]


The bottom line as now shown on both lists is that we have 13 k's remaining, 11 of which have been tested to n=118K and the other 2 of which have been tested very high with Sierp base 4. This balances with the 14 odd k's that I said I had remaining previously minus the one removed from Sierp base 4.


Gary[/QUOTE]


Good work, Gary!

I agree for the three k's that must be eliminated because they yield a prime for n = 1 which is, indeed, an odd exponent!!

Here are the gathered results for +1, n even :

1) Remaining :

[CODE] k tested up to (n base 2)

23451 1950964
60849 1907154
[/CODE]

Indeed, all are from Sierpinski base 4 project.

2) Primes :

[CODE]2379*2^8114+1 is prime! Time: 85.883 ms.
8139*2^25954+1 is prime! by Citrix 01/02/05, 06:08AM
9609*2^5422+1 is prime! Time: 68.815 ms.
10281*2^7444+1 is prime! Time: 186.376 ms.
11709*2^6882+1 is prime! Time: 176.373 ms.
12711*2^5092+1 is prime! Time: 67.712 ms.
14661*2^91368+1 is prime! by Jean Penné 27/01/05, 10:03PM
15441*2^20584+1 is prime! by Footmaster 27/01/05, 03:17PM
17169*2^6450+1 is prime! Time: 168.967 ms.
21069*2^23006+1 is prime! by Footmaster 27/01/05, 03:51PM
21699*2^72874+1 is prime! by Footmaster 27/01/05, 06:43PM
23799*2^105890+1 is prime! by Ken_g6 29/01/05, 05:45PM
23901*2^11292+1 is prime! Time: 801.239 ms.
30579*2^48594+1 is prime! by Mark 28/01/05, 12:02AM
33771*2^178200+1 is prime! byJean Penné 29/01/05, 08:10PM
33879*2^378022+1 is prime! by Footmaster 20/06/05, 12:21PM
35889*2^7770+1 is prime! Time: 372.790 ms.
39231*2^13716+1 is prime! Time: 924.592 ms.
39759*2^4594+1 is prime! Time: 61.723 ms.
40269*2^8458+1 is prime! Time: 389.306 ms.
41289*2^13514+1 is prime! Time: 917.695 ms.
41709*2^80594+1 is prime! by geoff 29/01/05, 05:38AM
42717*2^905792+1 is prime! by Jean Penné 14/10/05, 08:18PM
44469*2^13134+1 is prime! Time: 841.834 ms.
51171*2^93736+1 is prime! by masser 31/01/05, 04:18PM
52419*2^4578+1 is prime! Time: 61.466 ms.
52701*2^6976+1 is prime! Time: 177.811 ms.
52839*2^32558+1 is prime! by masser 27/01/05, 11:19PM
53979*2^7590+1 is prime! Time: 367.499 ms.
55611*2^40212+1 is prime! by Citrix 29/01/05, 05:46PM
56019*2^8094+1 is prime! Time: 379.657 ms.
56139*2^4858+1 is prime! Time: 64.132 ms.
58791*2^79420+1 is prime! by Mystwalker 27/01/05, 11:21PM
60891*2^40144+1 is prime! by Jean Penné 29/01/05, 09:30AM
61371*2^12576+1 is prime! Time: 821.165 ms.
62391*2^5472+1 is prime! Time: 124.840 ms.
63411*2^72064+1 is prime! by Footmaster 31/01/05, 06:05PM
[/CODE]

Regards,
Jean

jasong 2008-01-16 11:23

If no one objects, I'd like to reserve 16734*4^n-1. That's base=4, k=16734, Riesel numbers(-1). I believe the n-values that need to be tested start at n=100K.

If there's a sieved file, I'd love to know about it. Also, if people would rather I sieve than LLR, I can do that to. I just ask that the digit length of the lowest untested value in the sieve file be no more than twice the digit length of any un-LLred value in a lower base. In that instance, I'd probably want to sieve a lower base.

gd_barnes 2008-01-16 17:44

+1 odd-n conjecture web page update document
 
1 Attachment(s)
Karsten,

Attached is a notepad document that is an update of the web page that you sent me via PM that has many primes filled in and some corrections for the +1 odd-n conjecture. 6 of the k's had primes at n=1; 3 of which already had a higher prime and 3 of which had no prime found.

This balances with the 13 k's remaining at n=118K shown earlier in this thread.


Gary

gd_barnes 2008-01-16 18:10

[quote=jasong;122939]If no one objects, I'd like to reserve 16734*4^n-1. That's base=4, k=16734, Riesel numbers(-1). I believe the n-values that need to be tested start at n=100K.

If there's a sieved file, I'd love to know about it. Also, if people would rather I sieve than LLR, I can do that to. I just ask that the digit length of the lowest untested value in the sieve file be no more than twice the digit length of any un-LLred value in a lower base. In that instance, I'd probably want to sieve a lower base.[/quote]

You got it. I haven't done any sieving on base 4 past my original testing limit of n=100K. Jean or Karsten, do you have a sieve file for Riesel base 4 k=16734?

Jasong, I'm not sure I quite follow you here about 2X length of LLR'd value of lower base. I can only speculate that you might like to save sieving/LLRing time if Riesel k=16734/2=8367 base 2 has known testing above n=200K (n=100K base 4) to avoid double-testing.

When setting up the pages, I checked all k's on bases that are powers of 2 for primes in the prime archives at the top-5000 site and at [URL="http://www.rieselprime.org"]www.rieselprime.org[/URL] (converted from base 2) before putting anything up for testing. As shown on the latter site, k=8367 has only been tested to n=10K base 2 (n=5K base 4) and has no primes that are odd-n so you're OK there.

I think this is a very good idea to reserve this base 4 vs. base 16. It is open for both bases. It would be a waste of time for someone to sieve/test k=16734 base 16 and then turn around and do it for base 4. Perhaps that's part of what you're referring to.

In this case, I'll show you as reserving k=16734 on both base 4 and base 16. Otherwise someone could duplicate you base 16.

One caviot...If you find an even-n prime base 4 (n==0mod4 base 2), that will also eliminate the k on base 16 and you could stop testing. But if you find an odd-n prime base 4 (n==2mod4 base 2), I would suggest deleting all odd-n's in your sieve file and continue from there looking for an even-n base 16 prime.

Of course it's your choice to continue on for base 16 but it's a way to kill two birds with one stone. :smile: You could even end up with two different top-5000 primes; one for each base! :grin:


Gary

gd_barnes 2008-01-19 00:00

I am also proposing that this thread be moved to the "Conjectures 'R Us" project thread.

As discussed with Jean, we will be adding the Riesel and Seirp base 2 even-n and odd-n conjectures as a subproject to our project.

As with the other threads, I'll wait a couple of days before requesting that this be moved.


Gary

Jean Penné 2008-01-19 14:44

Just for fun and curiosity...
 
To illustraste the dissymetry between +1, base 2 odd / even exponents, I tested k = 18534/2 = 9267 with even exponents.
In less than 48H, I found that :

9267*2^n+1 is prime for

n = 100, 1556, 1966, 2660, 4342, 4468, 5372, 39538, 65386, 142426

although for odd exponents, I am presently reaching n = 1983943 with no prime!

I will continue even n during some days, just for fun...

Jean

Jean Penné 2008-01-19 17:22

Gathered results for -1, base 2 even and odd n's
 
Here are my gathered rsults for k*2^n-1 even and odd exponents.

(I think all these results would be moved in the new projects as soon as possible...)

Even n's, 4 k's remaining to be tested :

[CODE] k tested up to (n base 2)

9519 562416
14361 318510
19401 262578
20049 265144
[/CODE]

Even n's, 19 primes found / known :

[CODE]Normalized As discovered Keller freq.
k n

2181 37890 2181*2^37890-1 is prime! Time : 3.036 sec. f15
6549 5076 6549*2^5076-1 is prime! Time : 35.101 ms. f12
8181 8018 8181*2^8018-1 is prime! Time : 71.021 ms. f12
8961 30950 8961*2^30950-1 is prime! Time : 2.395 sec. f14
11379 32252 11379*2^32252-1 is prime! Time : 2.594 sec. f14
12849 9788 12849*2^9788-1 is prime! Time : 150.938 ms. f13
14859 11228 14859*2^11228-1 is prime! Time : 173.080 ms. f13
15639 66328 15639*2^66328-1 is prime! Time : 11.412 sec. f16
16431 4198 16431*2^4198-1 is prime! Time : 71.150 ms. f12
17889 10628 17889*2^10628-1 is prime! Time : 169.037 ms. f13
21501 7286 21501*2^7286-1 is prime! Time : 68.104 ms. f12
26091 4198 26091*2^4198-1 is prime! Time : 25.548 ms. f12
26511 167154 26511*2^167154-1 is prime! Time : 124.567 sec. f17
26601 46246 26601*2^46246-1 is prime! Time : 5.842 sec. f15
30171 76286 30171*2^76286-1 is prime! Time : 15.664 sec. f16
31431 16942 31431*2^16942-1 is prime! Time : 153.476 ms. f14
31749 5040 31749*2^5040-1 is prime! Time : 35.640 ms. f12
31959 19704 31959*2^19704-1 is prime! Time : 638.666 ms. f14
35259 10540 35259*2^10540-1 is prime! Time : 165.366 ms. f13
[/CODE]

Odd n's, 31 k's remaining to be tested :

[CODE] k 2k tested up to (n-1 base 2)

6927 13854 261944
8367 16734 262044
30003 60006 261942
39687 79374 253076
46923 93846 50174
48927 97854 32872
53973 107946 33286
59655 119310 32880
75363 150726 65610
75873 151746 48586
79437 158874 32788
86613 173226 65582
99363 198726 65742
100377 200754 94060
103947 207894 47788
106377 212754 48224
114249 228498 33078
130383 260766 69970
130467 260934 68508
131727 263454 154104
133977 267954 54508
135567 271134 58004
144117 288234 60384
145257 290514 121452
147687 295374 53488
148323 296646 53126
154317 308634 53408
155877 311754 58384
161583 323166 53702
163503 327006 53678
172167 344334 262032
[/CODE]

Odd n's, 83 primes found / known :

[CODE]Normalized As discovered
k n
903 10227 1806*2^10226-1 is prime! Time : 467.128 ms.
2433 3 4866*2^2-1 = 19463 is prime!
4887 4289 9774*2^4288-1 is prime! Time : 31.737 ms.
5007 6765 10014*2^6764-1 is prime! Time : 132.857 ms.
5163 6183 10326*2^6182-1 is prime! Time : 141.222 ms.
7977 31265 15954*2^31264-1 is prime! Time : 4.011 sec.
9087 4741 18174*2^4740-1 is prime! Time : 90.434 ms.
10113 14535 20226*2^14534-1 is prime! Time : 707.671 ms.
15213 20311 30426*2^20310-1 is prime! Time : 1.643 sec.
19377 18677 38754*2^18676-1 is prime! Time : 781.275 ms.
21813 4283 43626*2^4282-1 is prime! Time : 375.998 ms.
22863 101135 45726*2^101134-1 is prime! Time : 45.990 sec.
25797 1 51594-1 is prime!
27957 21477 55914*2^21476-1 is prime! Time : 1.678 sec.
30357 65361 60714*2^65360-1 is prime! Time : 18.190 sec.
32937 8473 65874*2^8472-1 is prime! Time : 493.300 ms.
33837 4273 67674*2^4272-1 is prime! Time : 165.707 ms.
34533 32899 69066*2^32898-1 is prime! Time : 4.595 sec.
35193 12483 70386*2^12482-1 is prime! Time : 743.684 ms.
37227 1 74454-1 is prime!
44283 4439 88566*2^4438-1 is prime! Time : 465.176 ms.
46107 4277 92214*2^4276-1 is prime! Time : 465.330 ms.
52137 26309 104274*2^26308-1 is prime! Time : 2.757 sec.
55983 9851 111966*2^9850-1 is prime! Time : 714.703 ms.
56493 6891 112986*2^6890-1 is prime! Time : 377.827 ms.
59763 4611 119526*2^4610-1 is prime! Time : 486.253 ms.
60237 1 120474-1 is prime!
60747 1 121494-1 is prime!
61833 4651 123666*2^4650-1 is prime! Time : 313.346 ms.
15663 3 31326*2^2-1 = 125303 is prime!
63153 60295 126306*2^60294-1 is prime! Time : 16.792 sec.
64023 11431 128046*2^11430-1 is prime! Time : 938.154 ms.
66087 1 132174-1 is prime!
67737 4437 135474*2^4436-1 is prime! Time : 380.406 ms.
70743 49387 141486*2^49386-1 is prime! Time : 9.225 sec.
72327 17125 144654*2^17124-1 is prime! Time : 1.523 sec.
72993 23319 145986*2^23318-1 is prime! Time : 2.711 sec.
75093 15371 150186*2^15370-1 is prime! Time : 1.336 sec.
75387 5181 150774*2^5180-1 is prime! Time : 407.256 ms.
78933 11443 157866*2^11442-1 is prime! Time : 1.068 sec.
84807 7389 169614*2^47388-1 is prime! Time : 8.790 sec.
87735 4551 175470*2^4550-1 is prime! Time : 194.893 ms.
88623 13251 177246*2^13250-1 is prime! Time : 1.245 sec.
88743 4619 177486*2^4618-1 is prime! Time : 470.335 ms.
90567 6577 181134*2^6576-1 is prime! Time : 627.684 ms.
91671 8795 183342*2^8794-1 is prime! Time : 641.417 ms.
93507 5449 187014*2^5448-1 is prime! Time : 490.452 ms.
97323 52207 194646*2^52206-1 is prime! Time : 9.747 sec.
100053 28459 200106*2^28458-1 is prime! Time : 4.296 sec.
100353 5147 200706*2^5146-1 is prime! Time : 577.426 ms.
101823 4519 203646*2^4518-1 is prime! Time : 377.304 ms.
102993 48975 205986*2^48974-1 is prime! Time : 9.151 sec.
105123 5555 210246*2^5554-1 is prime! Time : 429.150 ms.
105837 5913 211674*2^5912-1 is prime! Time : 435.785 ms.
27003 3 54006*2^2-1 = 216023 is prime!
115167 8685 230334*2^8684-1 is prime! Time : 355.645 ms.
117303 4451 234606*2^4450-1 is prime! Time : 186.024 ms.
117867 4513 235734*2^4512-1 is prime! Time : 188.221 ms.
120387 5645 240774*2^5644-1 is prime! Time : 230.829 ms.
121557 11817 243114*2^11816-1 is prime! Time : 594.670 ms.
129747 18657 259494*2^18656-1 is prime! Time : 1.299 sec.
132507 4485 265014*2^4484-1 is prime! Time : 187.186 ms.
133023 9087 266046*2^9086-1 is prime! Time : 407.860 ms.
133947 1 267894-1 is prime!
134037 4421 268074*2^4420-1 is prime! Time : 186.659 ms.
142683 22371 285366*2^22370-1 is prime! Time : 1.966 sec.
144393 6567 288786*2^6566-1 is prime! Time : 252.434 ms.
144867 1 289734-1 is prime!
144957 6473 289914*2^6472-1 is prime! Time : 251.359 ms.
145587 1 291174-1 is prime!
148227 5997 296454*2^5996-1 is prime! Time : 235.853 ms.
148803 25019 297606*2^25018-1 is prime! Time : 2.232 sec.
152907 4365 305814*2^4364-1 is prime! Time : 186.700 ms.
154827 9113 309654*2^9112-1 is prime! Time : 408.607 ms.
39093 3 78186*2^2-1 = 312743 is prime!
157383 44059 314766*2^44058-1 is prime! Time : 7.957 sec.
167007 4901 334014*2^4900-1 is prime! Time : 202.140 ms.
167997 18705 335994*2^18704-1 is prime! Time : 1.300 sec.
169527 9329 339054*2^9328-1 is prime! Time : 419.792 ms.
169743 23791 339486*2^23790-1 is prime! Time : 2.079 sec.
170223 4187 340446*2^4186-1 is prime! Time : 184.676 ms.
170733 7307 341466*2^7306-1 is prime! Time : 319.059 ms.
171783 6759 343566*2^6758-1 is prime! Time : 256.343 ms.
[/CODE]

Regards,

Jean

gd_barnes 2008-01-20 06:50

Jean,

Very good! Nice work.

I resumed testing the Sierp odd-n conjecture on 2 cores yesterday starting from n=118K. I'm now up to n=175K. I found primes on 4 more k's, all of which came in one small grouping from n=156K-170K, as follows:

50433*2^156597+1
91437*2^161615+1
61137*2^162967+1
39297*2^169495+1


This leaves 9 k's remaining! :smile:

Testing will pause at n=200K while I sieve a new file for the remaining k's.

I will request that this thread be moved over to the conjectures project shortly.

It will probably be Monday/Tuesday before I can get the project/my site updated to include the info. for this. For the time being, Karsten is keeping good track of things.


Gary

Jean Penné 2008-01-20 20:29

[QUOTE=gd_barnes;123257]Jean,

Very good! Nice work.

I resumed testing the Sierp odd-n conjecture on 2 cores yesterday starting from n=118K. I'm now up to n=175K. I found primes on 4 more k's, all of which came in one small grouping from n=156K-170K, as follows:

50433*2^156597+1
91437*2^161615+1
61137*2^162967+1
39297*2^169495+1


This leaves 9 k's remaining! :smile:

Testing will pause at n=200K while I sieve a new file for the remaining k's.

I will request that this thread be moved over to the conjectures project shortly.

It will probably be Monday/Tuesday before I can get the project/my site updated to include the info. for this. For the time being, Karsten is keeping good track of things.


Gary[/QUOTE]


Many congrats for this work, Gary, it's very encouraging!

Regards,
Jean

kar_bon 2008-01-20 23:46

[b]to Gary and Jean:[/b]

i included all data from above in the online-page (you know where).
have a look and than i can make it available for all.

karsten

Jean Penné 2008-01-21 07:37

[QUOTE=kar_bon;123322][b]to Gary and Jean:[/b]

i included all data from above in the online-page (you know where).
have a look and than i can make it available for all.

karsten[/QUOTE]

Very nice work, Karsten!

But, indeed, I cannot continue to have 32 k's reserved, I have not computer power enough for that!

For now, I will try to continue to test the -1, odd n's up to 256K base 2 ( n <= 262144), so I will now unreserve :

k = 9519 (even n's, tested now up to n = 581680, no prime...)

(This is now a top 5000 candidate!)

and for odd n's :

k = 6927, 8367, 30003, 39687, 172167 (no prime, tested as you showed).

Best Regards,
Jean

kar_bon 2008-01-21 15:18

oh, i was a little to quick to try. don't know you want to continue the odd-1 search while i inserted your gathered results.
after half a day run (sieve and test) i found:

53973*2^198575-1 is prime! (only this k tested)

so one candidate less to search for you. sorry.

i marked all other k's as reserved by you for odd-1.

do you have sieve-files for the other k's for me to test further?

now this page is available under [URL="http://www.rieselprime.de/Related/LiskovetsGallot.htm"]www.rieselprime.de/Related/LiskovetsGallot.htm[/URL]

or use [URL="http://www.rieselprime.de"]www.rieselprime.de[/URL] -> left menu -> 'Others Projects' there.

Jean Penné 2008-01-21 18:35

[quote=kar_bon;123367]oh, i was a little to quick to try. don't know you want to continue the odd-1 search while i inserted your gathered results.
after half a day run (sieve and test) i found:

53973*2^198575-1 is prime! (only this k tested)

so one candidate less to search for you. sorry.

i marked all other k's as reserved by you for odd-1.

do you have sieve-files for the other k's for me to test further?

now this page is available under [URL="http://www.rieselprime.de/Related/LiskovetsGallot.htm"]www.rieselprime.de/Related/LiskovetsGallot.htm[/URL]
or use [URL="http://www.rieselprime.de"]www.rieselprime.de[/URL] -> left menu -> 'Others Projects' there.[/quote]


No problem! Congrats for finding this prime! My goal is presently to eliminate the "easy" k's (those which would not yield a top 5000 prime) as fast as possible.
I also found 2 primes :

48927 35861 --> 97854*2^35860-1 is prime! Time : 4.610 sec.
59655 43825 --> 119310*2^43824-1 is prime! Time : 8.195 sec.

so, I am encouraged to continue!

I have no sieved file for n > 256K base 2 presently...

Regards,
Jean

gd_barnes 2008-01-22 04:12

Sierp odd-n status update
 
I have now tested the Sierp odd-n conjecture to n=200K. No primes were found since my last post. So here are the 9 k's remaining:

[code]
k test limit
9267 1967862
32247 1780000 (per Sierp base 4 mini-drive at CRUS)
37953 200K
53133 200K
60357 200K
70467 200K
80463 200K
84363 200K
85287 200K
[/code]


I am now sieving the k's remaining for n=200K-600K.


Gary

Jean Penné 2008-01-22 07:17

Two more primes on Riesel odd n's
 
Two more primes on Riesel odd n's :

79437 35093 158874*2^35092-1 is prime! Time : 5.142 sec.
114249 48469 228498*2^48468-1 is prime! Time : 9.130 sec.

26 remaining for now, continuing!

Jean

Jean Penné 2008-01-22 20:01

Three new primes found on Riesel odd n's
 
46923 65175 93846*2^65174-1 is prime! Time : 27.638 sec.
75363 120595 150726*2^120594-1 is prime! Time : 112.778 sec.
75873 62419 151746*2^62418-1 is prime! Time : 26.485 sec.

Now 23 k's remaining!

Jean

kar_bon 2008-01-22 20:16

great work, Jean. go!
3 more steps closer to the proof!
and ... woooshhhh... results online!

gd_barnes 2008-01-23 08:23

Correction on Riesel odd-n
 
Karsten,

I'm doing some double-checks up to n=10K and then n=25K on all of the base 2 even-n and odd-n conjectures before incorporating them in my web pages. So far I've checked Riesel odd-n and Sierp odd-n. For Sierp odd-n, the only issues that I found were the n=1 primes already posted here. On Riesel odd-n, I found one error:

84807*2^7389-1 is shown as prime. I found no prime for n<10K for this k so I searched further and found that 84807*2^47389-1 is prime instead. Obviously a missed digit.


Thanks,
Gary

kar_bon 2008-01-23 08:31

ok, got it.
Jean's data post #18 contains:

84807 7389 169614*2^47388-1 is prime! Time : 8.790 sec.

and i copied only the first 2 numbers without looking behind!

fixed it. good to check twice!

gd_barnes 2008-01-24 06:40

Karsten/Jean please confirm limits & reservations
 
[quote=Jean Penné;123342]Very nice work, Karsten!


For now, I will try to continue to test the -1, odd n's up to 256K base 2 ( n <= 262144), so I will now unreserve :

k = 9519 (even n's, tested now up to n = 581680, no prime...)

Best Regards,
Jean[/quote]

[quote=Jean Penné;123219]Here are my gathered rsults for k*2^n-1 even and odd exponents.

(I think all these results would be moved in the new projects as soon as possible...)

Even n's, 4 k's remaining to be tested :

[code] k tested up to (n base 2)

9519 562416
14361 318510
19401 262578
20049 265144
[/code]

Regards,

Jean[/quote]


Jean and Karsten,

Based on the above, I got a little confused because there are differences in this testing shown and what is shown on Karsten's Liskovets-Gallot conjectures web page. My pages are also incorrect due to so many previous posts flying around on these k's for different bases so I am working to correct them. Here is what I think it should be for all related bases:

Riesel base 2 even-n:
k=9519, test limit 581680; now unreserved
k=14361, test limit 318510; reserved by Jean
k=19401, test limit 262578; reserved by Jean
k=20049, test limit 265144; reserved by Jean

Riesel base 4:
k=9519, test limit 290840; now unreserved
k=14361, test limit 159255; reserved by Jean
k=19401, test limit 131289; reserved by Jean
k=20049, test limit 132572; reserved by Jean

Riesel base 16:
k=9519, test limit 145420; now unreserved
k=20049, test limit 66286; reserved by Jean

(k=14361 and 19401 are trivial base 16)


Karsten,

Can you correct your Liskovets-Gallot conjectures web page for the above test limits and reservations?

Also, are you now working on any of these k's instead of Jean?


Thanks,
Gary

gd_barnes 2008-01-24 07:53

More limit and reservations questions
 
Karsten and Jean,

There are 3 more k's for Riesel base 2 ODD-n, base 4, and base 16 that I need to confirm statuses, reservations, and test limits. Here is what I show for k=13854, 16734, and 19464 and their coharts for Riesel base 2 odd-n k=6927 and 8367:

Riesel base 2 odd-n:
k=6927, test limit 261945; now unreserved
k=8367, test limit 262045; now unreserved

Riesel base 4:
k=13854, test limit 130972; now unreserved
k=16734; test limit 131022; now unreserved
k=19464; test limit ??; reserved by Jean

Riesel base 16:
k=13854, test limit 100000; now unreserved (I tested this one separately to n=100000 since we had a sieved file for it. Odd n's would still need testing separately up to n=200000 base 4)
k=16734, test limit 66511; now unreserved
k=19464, test limit ??; reserved by Jean


Can one or both of you verify that the above is correct?

My main question is for Jean:
What is your test limit on k=19464? There was an original post that stated n=93672 base 4. And then a later post that stated n=137000 base 2. Since the later post was a lower range, I've become confused.

Note that all of this is coming about since I'm now incorporating the base 2 even-n and odd-n conjectures into my web pages.


Thanks,
Gary

gd_barnes 2008-01-24 18:15

[quote=jasong;122939]If no one objects, I'd like to reserve 16734*4^n-1. That's base=4, k=16734, Riesel numbers(-1). I believe the n-values that need to be tested start at n=100K.

If there's a sieved file, I'd love to know about it. Also, if people would rather I sieve than LLR, I can do that to. I just ask that the digit length of the lowest untested value in the sieve file be no more than twice the digit length of any un-LLred value in a lower base. In that instance, I'd probably want to sieve a lower base.[/quote]


Jasong is unreserving Riesel base 4 k=16734. He is working on another unrelated effort.

This also unreserves Riesel base 2 odd-n k=8367 and Riesel base 16 k=16734.


Gary

gd_barnes 2008-01-24 18:17

Jasong has unreserved Riesel base 4 k=16734 per a post that I just now put in the reservations/statuses thread.

This also unreserves Riesel base 16 k=16734 and the Riesel base 2 odd-n conjecture of k=8367.

I have changed the above post accordingly.


Gary

Jean Penné 2008-01-24 20:12

Unreserving k=19464
 
1 Attachment(s)
[QUOTE=gd_barnes;123772]Karsten and Jean,

There are 3 more k's for Riesel base 2 ODD-n, base 4, and base 16 that I need to confirm statuses, reservations, and test limits. Here is what I show for k=13854, 16734, and 19464 and their coharts for Riesel base 2 odd-n k=6927 and 8367:

Riesel base 2 odd-n:
k=6927, test limit 261945; now unreserved
k=8367, test limit 262045; now unreserved

Riesel base 4:
k=13854, test limit 130972; now unreserved
k=16734; test limit 131022; now unreserved
k=19464; test limit ??; reserved by Jean

Riesel base 16:
k=13854, test limit 100000; now unreserved (I tested this one separately to n=100000 since we had a sieved file for it. Odd n's would still need testing separately up to n=200000 base 4)
k=16734, test limit 66511; now unreserved
k=19464, test limit ??; reserved by Jean


Can one or both of you verify that the above is correct?

My main question is for Jean:
What is your test limit on k=19464? There was an original post that stated n=93672 base 4. And then a later post that stated n=137000 base 2. Since the later post was a lower range, I've become confused.

Note that all of this is coming about since I'm now incorporating the base 2 even-n and odd-n conjectures into my web pages.


Thanks,
Gary[/QUOTE]

Gary,

I reserved k=19464 because I believed falsely it might be tested for Riesel odd n's (but 19463 is prime), so, I wish to unreserve it.
I tested it up to n = 262032 base 2, then I created a base 4 sieve file up to n=1048576 (1024K) base 4. I will make it available to users by attaching it here. It is sieved up to 49.58 billions.

Regards,
Jean

Jean Penné 2008-01-24 20:45

Riesel odd n's : 3 new k's eliminated.
 
3 new primes found :

130383 104123 260766*2^104122-1 is prime! Time : 71.272 sec.
131727 169621 263454*2^169620-1 is prime! Time : 79.613 sec.
135567 68325 271134*2^68324-1 is prime! Time : 23.265 sec.

20 k's remaining now...

Also, for Sierpinski base 4 / odd n's, I completed the test of k = 9267 up to 2,000,000 base 2 (the very last n is 1999615), no prime... so, I am unreserving this k.

Jean

gd_barnes 2008-01-25 20:56

I'm reserving Riesel base 4 k=13854, 16734, and 19464 for further testing up to about n=250K base 4. I'll sieve to n=500K and leave my files for others if no primes are found on one or more of the k's.

It will also be the same k's for Riesel base 16.

Karsten, this also means I'll be reserving k=6927 and 8367 for the Riesel base 2 odd-n conjecture.


Gary

gd_barnes 2008-01-25 20:57

Riesel odd-n reservations
 
Karsten,

Part of a post from the reservations thread...

I'm reserving Riesel base 4 k=13854, 16734, and 19464 for further testing up to about n=250K base 4.

This also means I'll be reserving k=6927 and 8367 for the Riesel base 2 odd-n conjecture and taking them to n=500K base 2.


Gary

mdettweiler 2008-01-25 22:10

[quote=gd_barnes;123943]I'm reserving Riesel base 4 k=13854, 16734, and 19464 for further testing up to about n=250K base 4. I'll sieve to n=500K and leave my files for others if no primes are found on one or more of the k's.

It will also be the same k's for Riesel base 16.

Karsten, this also means I'll be reserving k=6927 and 8367 for the Riesel base 2 odd-n conjecture.


Gary[/quote]
I thought that base 4 Riesel only covers the even n for base 2? Thus, wouldn't you be reserving it for the even-n conjecture?

gd_barnes 2008-01-26 10:06

[quote=Anonymous;123951]I thought that base 4 Riesel only covers the even n for base 2? Thus, wouldn't you be reserving it for the even-n conjecture?[/quote]

No, it also covers odd-n IF the k base 4 is divisible by 2, i.e.

Let k=2m and let n=q

2m*4^q-1 = 2m*2^(2q)-1 = m*2^(2q+1)-1

Hence where the base is 4 and k=2m, then where the base is 2, n must be 2q+1; hence odd.

In this case, k=13854 and k=16734 base 4 equate to k=6927 and k=8367 base 2 odd-n.

It's surprising how tricky it has been to keep all of our reservations clean and consistent across all bases without stepping on one another; namely the bases that are powers of 2.

Edit: One more requirement...the k base 4 cannot be divisible by 4 in order to 'reduce' to a base 2 odd-n k. The even-n and odd-n conjectures have a requirement that the k must be odd and divisible by 3 or...as shown on my pages k==3 mod 6.


Gary

mdettweiler 2008-01-26 16:20

[quote=gd_barnes;123994]No, it also covers odd-n IF the k base 4 is divisible by 2, i.e.

Let k=2m and let n=q

2m*4^q-1 = 2m*2^(2q)-1 = m*2^(2q+1)-1

Hence where the base is 4 and k=2m, then where the base is 2, n must be 2q+1; hence odd.

In this case, k=13854 and k=16734 base 4 equate to k=6927 and k=8367 base 2 odd-n.

It's surprising how tricky it has been to keep all of our reservations clean and consistent across all bases without stepping on one another; namely the bases that are powers of 2.

Edit: One more requirement...the k base 4 cannot be divisible by 4 in order to 'reduce' to a base 2 odd-n k. The even-n and odd-n conjectures have a requirement that the k must be odd and divisible by 3 or...as shown on my pages k==3 mod 6.


Gary[/quote]
Okay, thanks for the explanation. :smile:

tnerual 2008-01-27 14:12

[QUOTE=gd_barnes;123888]Go Tnerual go! 7707 k's...wow. Good luck! :smile:


G[/QUOTE]

now at n=2414 ... 4960 k's remaining

stopping for 10 days ... hollidays :smile:

all computers switched back to llrnet CRUS1

Gary, can you tag sierp31 as reserved :wink:

see you next week

tnerual

gd_barnes 2008-01-28 08:39

A big one drops for odd-n...
 
From the 'regular' primes thread:

Base 2 odd-n:
8367*2^313705-1 :smile:

I'm still working on Base 2 odd-n k=6927. I'm currently at n=324K base 2.


Gary

kar_bon 2008-01-28 10:12

Riesel base 6
 
40657*6^39087-1 is prime (status see other thread)

Jean Penné 2008-01-28 16:46

Gongrats, Gary! Two more prime for me for R. odd n
 
Very good news, Gary, and many congrats!

I also found two more primes in my range :

100377 231813 200754*2^231812-1 is prime! Time : 151.901 sec.
161583 138711 323166*2^138710-1 is prime! Time : 157.329 sec.

Also, I reached my 256K limit for :

k = 86613, n = 262111, no prime...
k = 163503, n = 262107, no prime...

So, I am unreserving these two k's for now.

After your last discovery, there are now 17 k's remaining, 6 of them I tested up to n <= 256K.
Regards,
Jean

gd_barnes 2008-01-31 18:36

Status on double-check
 
[quote=gd_barnes]
2. I have to rerun the entire batch for k=16734 and k=19464 on a different machine to see if I missed any primes. (not bad; ~2 CPU days)
3. I have to rerun the entire batch for n=100K-104K for Sierp base 16 on a different machine(s) looking for missing primes. (bad bad; ~10-12 CPU days)
[/quote]

Status on this double-check:

k=13854, 16734, and 19464 for Riesel base 4 have now been double-checked up to their original limit on n=324K. No missing primes were found and the one k=16734 prime was confirmed.

k=13854 and 19464 have been sieved higher and are now continuing on from there.

n=100K-104K for Sierp base 16 is about half-done and should be complete ~Monday-Tuesday. No missing primes so far.


Gary

Jean Penné 2008-02-01 20:01

Riesel base 2 - odd n's, unreserving 4 k's
 
I reached the 256K n limit for 4 new k's, so I will unreserve these k's for now :

k = 99363, last n = 262143
k = 103947, last n = 261941
k = 106377, last n = 262065
k = 130467, last n = 262109

No new primes...

I shall be abroad for two weeks, but I hope my 7 remaining tests will be completed when going back...

Regards,
Jean

em99010pepe 2008-02-01 22:07

[quote=gd_barnes;124548]
Were you running this on a slower machine?[/quote]

Yes.

gd_barnes 2008-02-03 09:32

Riesel base 2 odd-n status
 
k=6927 now at n=414K; no primes

testing to n=500K base 2 in conjunction with Riesel base 4 k=13854

gd_barnes 2008-02-03 09:41

Status on 2 k's for Riesel base 4
 
Riesel base 4 k=13854 and 19464 now at n=207K base 4. No primes.

This also means that Riesel base 16 same k's are now at n=103.5K.

Going to at least n=250K base 4.

gd_barnes 2008-02-03 10:25

Sierp base 2 odd-n status
 
k=37953, 53133, 60357, 70467, 80463, 84363, 85287 all at n=224K.

All going to n=600K or until a prime is found.

gd_barnes 2008-02-06 22:32

Riesel base 4 and 16 status on 2 reserved k's
 
For Riesel base 4 k=13854 and 19464, I am at n=250K. I decided to go ahead and take them through n=300K.

This means that for the same k's on Riesel base 16, I'm at n=125K.

gd_barnes 2008-02-06 22:47

Riesel and Sierp odd-n statuses
 
Riesel base 2 odd-n k=6927 now at n=500K; no primes. I'll up my test limit to n=600K base 2 in conjunction with Riesel base 4 k=13854.


Sierp base 2 odd-n k=37953, 53133, 60357, 70467, 80463, 84363, & 85287 all at n=250K; no primes. Still going to n=600K on all.


Gary

gd_barnes 2008-02-11 20:42

Sierp odd-n prime and status
 
[SIZE=2]Sierp base 2 odd-n:[/SIZE]
[SIZE=2]70467*2^268503+1 is prime[/SIZE]

[SIZE=2]Sierp base 2 odd-n k=37953, 53133, 60357, 80463, 84363, & 85287 all now at n=286K.[/SIZE]


[SIZE=2]Gary[/SIZE]

gd_barnes 2008-02-14 20:45

[SIZE=2]Sierp base 2 odd-n:[/SIZE]
[SIZE=2]37953*2^298913+1 is prime[/SIZE]

Now down to 7 k's remaining.

[SIZE=2]Sierp base 2 odd-n k=53133, 60357, 80463, 84363, & 85287 are all now at n=305K; still going to n=600K.[/SIZE]

Note: I have been double-checking k=9267 and 32247 along with this so I still have 7 k's in my sieved file. I'll double-check them to n=600K along with the rest. If I decide to continue higher than n=600K with the other k's, I'll drop the double-checking of the 2 k's at that point.


[SIZE=2]Gary[/SIZE]

gd_barnes 2008-02-14 20:49

Riesel base 4 and 16 status on 2 reserved k's
 
Riesel base 4 k=13854 and 19464 are complete to n=300K. No primes. They are now unreserved.

This means that the same k's on Riesel base 16 are completed to n=150K and are also unreserved.

gd_barnes 2008-02-14 20:51

Riesel base 2 odd-n status
 
Riesel base 2 odd-n k=6927 is now complete to n=600K and unreserved. No primes.

It had been tested in conjunction with base 4 k=13854.

kar_bon 2008-02-15 01:16

even Riesel:
k=14361, 19401 and 20049 at n=300k (even)

Jean Penné 2008-02-18 17:27

Another Riesel base 2 - odd n prime.
 
On 01/02/2008, I found :

288234*2^224976-1 is prime! Time : 290.692 sec.

which is 144117*2^224977-1

Now, only 16 k's are remaining

All these remaining k's have been tested at least up to n = 256K (262144).

Jean

Jean Penné 2008-02-18 18:23

New status for Riesel base 2 odd n
 
From "regular" primes thread :

288234*2^224976-1 is prime! Time : 290.692 sec.

which is 144117*2^224977-1

Now, only 16 k's are remaining

Also, I reached the 256K limit for :

k = 133977, n = 262029, no prime
k = 145257, n = 261781, no prime
k = 147687, n = 261881, no prime
k = 148323, n = 262079, no prime
k = 154317, n = 262065, no prime
k = 155877, n = 262085, no prime

So, I am unreserving these k's for now (but perhaps would reserve some of them later...).

Regards,
Jean

gd_barnes 2008-02-18 20:16

[quote=Jean Penné;126068]On 01/02/2008, I found :

288234*2^224976-1 is prime! Time : 290.692 sec.

which is 144117*2^224977-1

Now, only 16 k's are remaining

All these remaining k's have been tested at least up to n = 256K (262144).

Jean[/quote]

Jean,

Welcome back from vacation! It's always nice to come back to a prime. :smile:

Per a previous posting, I show k=39687 only tested to n=253.1K. Is that correct?


Thanks,
Gary

Jean Penné 2008-02-18 22:02

Yes, I forgot it!
 
[QUOTE=gd_barnes;126082]Jean,

Welcome back from vacation! It's always nice to come back to a prime. :smile:

Per a previous posting, I show k=39687 only tested to n=253.1K. Is that correct?


Thanks,
Gary[/QUOTE]

You are perfectly right, Gary, I forgot to complete this one!!
I am restarting it now from this point...

Thanks,
Jean

Jean Penné 2008-02-19 15:24

k = 39687 now tested up to 256K (Riesel odd n's)
 
[QUOTE=Jean Penné;126087]You are perfectly right, Gary, I forgot to complete this one!!
I am restarting it now from this point...

Thanks,
Jean[/QUOTE]

Completed :
k = 39687, n = 261837, no prime...

so, I am also unreserving this k for now.
I shall now try to make some further sieving on the 16 remaining k's...
Regards,
Jean

Jean Penné 2008-02-19 20:59

New status for Sierpinski base 2 - even n's
 
Here is to-day's status for Sierpinski base 2 - even n's (which is half of remaining k's for Sierpinski base 4) :

k = 23451 is up to n = 1,977,272 no prime...

k = 60849 is up to n = 1,940,034 no prime...

Regards,
Jean

Jean Penné 2008-02-20 16:39

Riesel base 2 odd n's sieving ; reserving one k
 
I am now sieving the 16 remaining k's for Riesel base 2 odd n's (in conjonction with Riesel base 4) from n = 256K to 2048K base 2, using srsieve, and shall distribute the sieve files in Newpgen format when sieved enough(at least p = 100 billions)...

For now, I wish to reserve again k = 155877 (in conjonction with k = 311754 for base 4) for LLR testing up to n = 512K (524288) base 2, or, I hope, prime found below...

Regards,
Jean

gd_barnes 2008-02-20 17:01

[quote=Jean Penné;126252]I am now sieving the 16 remaining k's for Riesel base 2 odd n's (in conjonction with Riesel base 4) from n = 256K to 2048K base 2, using srsieve, and shall distribute the sieve files in Newpgen format when sieved enough(at least p = 100 billions)...

For now, I wish to reserve again k = 155877 (in conjonction with k = 311754 for base 4) for LLR testing up to n = 512K (524288) base 2, or, I hope, prime found below...

Regards,
Jean[/quote]

Great! The sieve files help a lot. Perhaps we'll can make a mini-drive out of it.

Do you know that I tested Riesel base 2 odd-n k=6927 to n=600K base 2? That was done in conjuction with Riesel base 4 k=13854 to n=300K base 4. But if you want to include the range as a double-check in your sieved file(s), that works for me.


Gary

Jean Penné 2008-02-20 17:39

[QUOTE=gd_barnes;126254]Great! The sieve files help a lot. Perhaps we'll can make a mini-drive out of it.

Do you know that I tested Riesel base 2 odd-n k=6927 to n=600K base 2? That was done in conjuction with Riesel base 4 k=13854 to n=300K base 4. But if you want to include the range as a double-check in your sieved file(s), that works for me.


Gary[/QUOTE]

Yes, I know that, and it is great! We may use the corresponding sieved file for double-checking, or starting after your upper limit...

Jean

Jean Penné 2008-02-24 19:26

Riesel base 2 odd n's ; reserving another k.
 
I wish to reserve k = 39687 (in conjonction with k = 79374 for base 4) for LLR testing up to n = 512K (524288) base 2, or, I hope, prime found below...
Jean

P.S. My sieving is progressing fine...

Jean Penné 2008-02-29 18:17

Riesel base 2 odd n's status ; sieved files
 
To-day :

k = 39687 is tested up to n = 416853, no prime.

k = 155877 is tested up to n = 400351, no prime.

The 16 files (for n = 256K to 2048K) are now sieved to 235 billions ;

I am abroad for a week and shall send them when going back.
Jean

gd_barnes 2008-02-29 20:27

Sierp base 2 odd n status
 
Sierp base 2 odd-n all remaining 7 k's now at n=365K, 2 of which are being double-checked.

Nothing to report.

gd_barnes 2008-03-10 21:31

Sierp base 2 odd-n status
 
Sierp base 2 odd-n all remaining 7 k's now at n=414K, 2 of which are being double-checked.

Nothing to report.

Jean Penné 2008-03-12 17:39

Riesel base 2 odd n's status ; sieved files
 
Hello,

To-day :

k = 39687 is tested up to n = 494637, no prime, continuing up to 512K.

k = 155877 is tested up to n = 527237, no prime, so, I am unreserving this k.
I wish to reserve k = 133977 in place.

The 16 files (for n = 256K to 2048K) are now sieved to 569.7 billions ;
They are available for downloading from my personal site, at URL :

[url]http://jpenne.free.fr/ConjRus/[/url]

I am continuing the sieving and shall update these files on place when 1 Tera reached.

Regards,
Jean

Jean Penné 2008-03-17 16:05

[QUOTE=Jean Penné;128685]Hello,

To-day :

k = 39687 is tested up to n = 494637, no prime, continuing up to 512K.

k = 155877 is tested up to n = 527237, no prime, so, I am unreserving this k.
I wish to reserve k = 133977 in place.

The 16 files (for n = 256K to 2048K) are now sieved to 569.7 billions ;
They are available for downloading from my personal site, at URL :

[url]http://jpenne.free.fr/ConjRus/[/url]

I am continuing the sieving and shall update these files on place when 1 Tera reached.

Regards,
Jean[/QUOTE]

To-day :

k = 39687 is tested up to n = 535677, no pime, so I am releasing this k.
(The machine I used for it beeing not perfectly reliable, I think this k needs a double-check in range 256K to 512K)
I quoted my previous message to make a reminder about it.
Jean

gd_barnes 2008-03-21 04:38

Sierp base 2 odd-n status
 
Sierp base 2 odd-n all remaining 7 k's now at n=445K, 2 of which are being double-checked.

Nothing to report.

Jean Penné 2008-03-23 20:26

Sierp. b. 2 even n's, Riesel b. 2 odd n's status
 
Sierpinski base 2 even n's / Sierpinski base 4 :

I reached the 2M limit for k = 23451, no prime...
The last exponent tested was n = 1,999,922
I am unreserving this k for now.

k = 60849 is now tested up to n = 1,965,606, no prime, continuing up to 2M...

To continue this work further, we need now much sieving, so I decided to start a big sieve operation :

I launched the Srsieve program with an input file containing the 9 remaining k's for Sierpinski base 2 even n's (2 k's) and odd n's (7 k's) and the range of n = 1 to 8,388,608 base 4, which is 16M base 2 !
I wish to continue this work on one machine as long as needed, so the resulting sieved files might be splitted and distributed from time to time to users when sieved enough, both for first or double checking...
Suggestions for organizing the distribution would be welcome!

Riesel Base 2 odd n's :

k = 133977 is now tested up to n = 491633, no prime, continuing up to 512K
I am starting to test k = 86613 from 256 to 512K, so I reserve it for now.

A reminder :
The 16 files (for n = 256K to 2048K) are now sieved to 569.7 billions ;
They are available for downloading from my personal site, at URL :

[url]http://jpenne.free.fr/ConjRus/[/url]

I am continuing the sieving and shall update these files on place when 1 Tera reached.

Regards,
Jean

Jean Penné 2008-03-26 21:14

Riesel Base 2 odd n's status
 
Riesel Base 2 odd n's to-day :

k = 133977 is up to n = 524429 no prime, so I unreserve this k...
k = 86613 is up to n = 348807 no prime, continuing up to 512K

Reserving now k = 148323 up to n = 512K

Regards,
Jean

Jean Penné 2008-03-28 17:42

Riesel base 2 odd n's status
 
As I reported on an other thread here, k = 86613 is eliminated, because :

86613*2^356967-1 is prime! (code L591) ; now 15 k's are remaining.

I am presently testing two k's :

k = 145257 is up to n = 304853
k = 148323 is up to n = 331647

The 16 presieved files are now sieved up to p = 1.018 tera, so I updated them on my personal site :

[url]http://jpenne.free.fr/ConjRus/[/url]

I am continuing the sieving only on the 15 remaining k's, so it becomes faster.

Karsten, do you intend to update the data on the Liskovets-Gallot page of Riesel Prime Search soon? There are pretty many changes to report!
Thank you by advance, and Best Regards,
Jean

kar_bon 2008-03-31 07:28

Riesel base 2 odd n
 
found this 2 days ago:
(thanks Jean for correction)
198726*2^268878-1 = 198726*4^134439-1 = 99363*2^268879-1

and today

260934*2^273436-1 = 260934*4^136718-1 = 130467*2^273437-1

so there're 13 k's remaining!

by now all these 13 k's tested upto n=274,000 -> odd n=137,000!

kar_bon 2008-03-31 07:56

i updated the page with all information from last posts!

thanks Jean for the sieving files for Riesel odd n, so another 2 k's kicked out (see above)!

kar_bon 2008-03-31 07:59

Riesel base 2 odd
 
198726*2^268878-1 = 198726*4^134439-1 = 99363*2^268879-1

and

260934*2^273436-1 = 260934*4^136718-1 = 130467*2^273437-1

Jean Penné 2008-03-31 13:45

Very nice results!
 
Many congrats, Gary and Karsten, for these last three primes, there are very nice results, because 1 k is eliminated for Sierpinski base 2 odd n's and 2 k's are eliminated for Riesel base 2 odd n's.

Moreover, the big sievings I started for these two sub-projects will become a lot faster!

Please, Karsten would you credit yourself, (instead of me) for the two primes you discovered!

Best Regards,
Jean

Jean Penné 2008-03-31 16:46

More sieving...
 
[QUOTE=kar_bon;130331]i updated the page with all information from last posts!

thanks Jean for the sieving files for Riesel odd n, so another 2 k's kicked out (see above)![/QUOTE]

Thank you Karsten!
I am also continuing to sieve, on another machine, the 8 remaining files for Sierpinski base 2 even and odd n's (which also cover the complete Sierpinski base 4 project).
As I chose a large range (n = 1 to 16M base 2), the progress is slower, but I am already reaching 70 billions ; I shall make a first distribution when 100 billions reached.
These data will be usable both for testing and double-checking...
Regards,
Jean

gd_barnes 2008-04-01 04:13

[quote=kar_bon;130329]found this 2 days ago:
(thanks Jean for correction)
198726*2^268878-1 = 198726*4^134439-1 = 99363*2^268879-1

and today

260934*2^273436-1 = 260934*4^136718-1 = 130467*2^273437-1

so there're 13 k's remaining!

by now all these 13 k's tested upto n=274,000 -> odd n=137,000![/quote]

Based on this, I am reserving for Karsten all remaining k's that are not already reserved by Jean and showing them as tested to n=274K.

odd n=137000 ??? I hope not.

Do you mean base 4 n=137000? :smile:


This brings up something that has caused a little confusion in the past:

Can I request that we stick with a specific standard when showing primes or search-ranges? That standard should be whatever base the conjecture is and whatever the k is for the conjecture is how we should state testing limits or primes. I don't understand the redundancy of showing the even-k/even-n and the base 4 primes here when we're proving odd-k/odd-n for base 2.

The only exception might be if the k is remaining on both base 2 and base 4, which is usually not the case, especially for Riesel base 2 odd-n with a high conjecture.

Here, just stating 99363*2^268879-1 and 130467*2^273437-1 as prime with a testing limit of n=274K base 2 on all k's should be all that is needed.


Thanks,
Gary

Jean Penné 2008-04-01 06:27

[QUOTE=gd_barnes;130437]Based on this, I am reserving for Karsten all remaining k's that are not already reserved by Jean and showing them as tested to n=274K.

odd n=137000 ??? I hope not.

Do you mean base 4 n=137000? :smile:


This brings up something that has caused a little confusion in the past:

Can I request that we stick with a specific standard when showing primes or search-ranges? That standard should be whatever base the conjecture is and whatever the k is for the conjecture is how we should state testing limits or primes. I don't understand the redundancy of showing the even-k/even-n and the base 4 primes here when we're proving odd-k/odd-n for base 2.

The only exception might be if the k is remaining on both base 2 and base 4, which is usually not the case, especially for Riesel base 2 odd-n with a high conjecture.

Here, just stating 99363*2^268879-1 and 130467*2^273437-1 as prime with a testing limit of n=274K base 2 on all k's should be all that is needed.


Thanks,
Gary[/QUOTE]


Gary,
I am now totally confused about the reservations for this sub-project :
Do you mean that now, I may not reserve any more k's for this sub-project?
So, I should be forced to keep the three k's I am working on for ever, and I think it is not a good strategy! (that is what I did for two years on Sierpinski base 4, and I don't wish to continue this way...) On the contrary, I think that when the exponents become so large (and the chance to find a prime so small) it is better to split the presieved files so the provers can take small ranges...
I need more specifications about this...
Regards,
Jean

gd_barnes 2008-04-01 08:16

No, I'm not talking about reservations here. You can reserve any k you want in any base. You can reserve as many k's or bases that you can test! :smile: I'm only referring to POSTING of primes and ranges completed.

I'm saying that when you and Karsten post a prime or a range completed, please just post it in the format of the Conjectured k, base, and exponent and leave out forms of the primes and ranges that don't pertain the specific conjecture(s).

Here's an example on Karsten's post:

[quote]
198726*2^268878-1 = 198726*4^134439-1 = 99363*2^268879-1

and today

260934*2^273436-1 = 260934*4^136718-1 = 130467*2^273437-1

so there're 13 k's remaining!

by now all these 13 k's tested upto n=274,000 -> odd n=137,000!
[/quote]


My question is why are we showing 3 different forms of the same prime? These k's are not remaining for anything else except riesel odd-n. So...what I'm asking is that we keep the prime and ranges posts short and simple with:

[quote]
99363*2^268879-1 is prime

and today
130467*2^273437-1 is prime

so there're 13 k's remaining!

all these 13 k's now tested up to n=274,000
[/quote]


In this case, we are not testing even k's, we're not testing even n's, and we're not testing base 4. We're just testing Riesel base 2 odd-n.

So there's no reason to state the even k's, even n's, or base 4 forms of the primes.

Now...if one test covers more than one base or conjecture, THEN it makes sense to state them in more than one way. For instance k=9519 for base 2 even-n and for base 4.

I hope this clarifies the request.

Please know that this isn't a requirement...it's only a suggestion. I'm asking because I've actually posted the incorrect n-value for a prime on my pages when reading one of these previously. I then caught it the next day.

Also, I would never limit anyone from searching anything as long as they are providing regular updates. That's the fastest way to lose people from a project.


Thanks,
Gary


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