Riesel and Sierp numbers bases <= 1024
 

I've done some search on the sierpinski side up to base=1024,
see: [URL="http://robert.gerbicz.googlepages.com/sierpinski.txt"]http://robert.gerbicz.googlepages.com/sierpinski.txt[/URL]

Better Riesel values, also up to base=1024:
[URL="http://robert.gerbicz.googlepages.com/riesel.txt"]http://robert.gerbicz.googlepages.com/riesel.txt[/URL]

I've converted the conjectures to a spreadsheet format for easy sorting by conjecture size. Attached are the two files in .csv format. Maybe someone else will find them useful. :smile:

[quote=Mini-Geek;199009]I've converted the conjectures to a spreadsheet format for easy sorting by conjecture size. Attached are the two files in .csv format. Maybe someone else will find them useful. :smile:[/quote]

I think somebody should start on Riesel base 280. :smile:

That brings up several interesting questions: Is Riesel base 280 the highest known conjecture? Is it the highest possible conjecture for any base? Do we know for sure that there is not a smaller conjecture with a period > 36 like what happened with base 3, which has a period of 144?

Perhaps Mr. Gerbicz might have some answers for us there.

A couple of interesting notes: (1) Despite the many huge conjectures, the median conjecture is k=208 on both sides. (2) The smallest odd conjecture is k=13. I realize that lower odd conjectures are possible but there doesn't happen to be any for bases <= 1024.

[quote=gd_barnes;199200]Do we know for sure that there is not a smaller conjecture with a period > 36 like what happened with base 3, which has a period of 144?[/quote]
[code]E:\OurDocuments\Mersenne\covering>covering
144 280 -1 100000 513613045571842
Checking k*280^n-1 sequence for exponent=144, bound for primes in the covering set=100000, bound for k is 513613045571842
Examining primes in the covering set: 281,26227,78401,78121,17,13,9133,51769,19,37,433,18313,73,97,38833,23761,61057
And their orders: 2,3,4,6,8,12,12,12,18,18,18,24,36,48,48,144,144
**************** Solution found ****************
482870640360662
**************** Solution found ****************
371284522956233
**************** Solution found ****************
253971311388192

E:\OurDocuments\Mersenne\covering>covering
72 280 -1 100000 513613045571842
Checking k*280^n-1 sequence for exponent=72, bound for primes in the covering set=100000, bound for k is 513613045571842
Examining primes in the covering set: 281,26227,78401,78121,17,13,9133,51769,19,37,433,18313,73
And their orders: 2,3,4,6,8,12,12,12,18,18,18,24,36
**************** Solution found ****************
513613045571841
[/code]whats strange is that an exponent of 72 finds 513613045571841 but 144 doesnt
is this a bug in the covering program?

[QUOTE]I think somebody should start on Riesel base 280. :smile:[/QUOTE]

I'm crazy but not that crazy. Too bad the covering program limits us to 1 set of parameters at a time otherwise we could look WAY OUT at the bases > 1024 on both sides.

i was just looking at riesel base 280 last night,and was thinking it would be a good idea to start some sort of effort on it.i might do so work on it at a later stage.

144 produces
[code]**************** Solution found ****************
482870640360662
**************** Solution found ****************
371284522956233
**************** Solution found ****************
253971311388192[/code]288 produces
[code]**************** Solution found ****************
203047772514813
**************** Solution found ****************
179533651185182
**************** Solution found ****************
106286297574924
**************** Solution found ****************
41294807980463
**************** Solution found ****************
31741813281359
not finished yet[/code]120 produces
[code]**************** Solution found ****************
367930956102524
**************** Solution found ****************
12775672337441[/code]360 and 240 are running(walking actually:smile:)
looks like adding a factor of 5 into the exponent is helpful sometimes
i would be half surprised if 12775672337441 turns out to be the lowest value

[quote=henryzz;199209]120 produces
[code]**************** Solution found ****************
367930956102524
**************** Solution found ****************
12775672337441[/code]360 and 240 are running(walking actually:smile:)
looks like adding a factor of 5 into the exponent is helpful sometimes
i would be half surprised if 12775672337441 turns out to be the lowest value[/quote]
With this, Riesel 280's conjecture has dropped below Riesel 15 and 511. The 5 highest conjectures, (which are all 5 greater than 10^13) on both sides, are now:[code]S15: 91218919470156
S280: 82035074042274
R511: 40789000085994
R15: 36370321851498
R280: 12775672337441
[/code]S15, with a prime bound of 100K, has no lower solutions for exponent 144. I'm currently checking 120 to 100K and 360 to 10K. I'm also checking S280 with exponent 120 and a 100K bound.

I think none of the posted riesel k values for base=280 is good. Or am I wrong?

k=513613045571842 is still good. For such large searches the program can print out bad values, the reason is that when bound_for_k*bound_for_primes is very large, say about 2^60 or so. Here the order of the primes in the covering set is also important, because for the original k value p=78121 is in the covering set, but the code has found this solution. The solution would be to rewrite this in gmp to eliminate all such limitations. (I don't have time for this).

It wouldn't be bad to check all k values for bases<=1024 for both sides. I'm not sure if I've done this.

ps. OK, checked this in gmp, there is no wrong k values in the two files.

[quote=R. Gerbicz;199215]I think none of the posted riesel k values for base=280 is good. Or am I wrong?

k=513613045571842 is still good. For such large searches the program can print out bad values, the reason is that when bound_for_k*bound_for_primes is very large, say about 2^60 or so. Here the order of the primes in the covering set is also important, because for the original k value p=78121 is in the covering set, but the code has found this solution. The solution would be to rewrite this in gmp to eliminate all such limitations. (I don't have time for this).

It wouldn't be bad to check all k values for bases<=1024 for both sides. I'm not sure if I've done this.

ps. OK, checked this in gmp, there is no wrong k values in the two files.[/quote]
based on this i have stopped my runs

Here are some notes about the outputs from David's runs:

12775672337441*280^7-1 is prime
367930956102524*280^2-1 is prime
31741813281359*280^1-1 is prime
41294807980463*280^3-1 is prime
179533651185182*280^9-1 is prime
203047772514813*280^14-1 is prime
253971311388192*280^4-1 is prime
371284522956233*280^404-1 is prime
482870640360662*280^10-1 is prime

So those can't have a covering set.

k=106286297574924 was the only one that I couldn't find a prime for (up to n=2500). But since n=2 has a smallest factor of 11229577 and n=7 has a smallest factor 14 digits long, it is unlikely to have a full covering set.

[quote=gd_barnes;199285]k=106286297574924 was the only one that I couldn't find a prime for (up to n=2500). But since n=2 has a smallest factor of 11229577 and n=7 has a smallest factor 14 digits long, it is unlikely to have a full covering set.[/quote]
In any case, the bounds were likely set to 100000, allowing a max prime length of 5, so if it does have a covering set, it wasn't detected properly.

[quote=Mini-Geek;199288]In any case, the bounds were likely set to 100000, allowing a max prime length of 5, so if it does have a covering set, it wasn't detected properly.[/quote]
yes the bounds were set to 100k for all my runs
i did notice something weird which i now think was probably due to overflows
if i lowered the max k bound too far it wouldnt find a solution that was still below the max k bound

[QUOTE=gd_barnes;199285]Here are some notes about the outputs from David's runs:

12775672337441*280^7-1 is prime
367930956102524*280^2-1 is prime
31741813281359*280^1-1 is prime
41294807980463*280^3-1 is prime
179533651185182*280^9-1 is prime
203047772514813*280^14-1 is prime
253971311388192*280^4-1 is prime
371284522956233*280^404-1 is prime
482870640360662*280^10-1 is prime

So those can't have a covering set.

k=106286297574924 was the only one that I couldn't find a prime for (up to n=2500). But since n=2 has a smallest factor of 11229577 and n=7 has a smallest factor 14 digits long, it is unlikely to have a full covering set.[/QUOTE]

In fact you don't need to find primes/divisors to prove that the k value is good or not, the following quick pari code decide this:
[code]
F(k,b,c,period)=if(gcd(k+c,b-1)>1,return(0));\
for(n=1,period,if(gcd(k*b^n+c,b^period-1)==1,return(0)));return(1)
[/code]

it checks the k*b^n+c sequence for a given period without factorization. For example F(482870640360662,280,-1,144)=0 (false) and F(513613045571841,280,-1,36)=1 (so true)
and F(4,7,-1,1)=0 (false, trivial factor(s)).

[quote=R. Gerbicz;199215]I think none of the posted riesel k values for base=280 is good. Or am I wrong?

k=513613045571842 is still good. For such large searches the program can print out bad values, the reason is that when bound_for_k*bound_for_primes is very large, say about 2^60 or so. Here the order of the primes in the covering set is also important, because for the original k value p=78121 is in the covering set, but the code has found this solution. The solution would be to rewrite this in gmp to eliminate all such limitations. (I don't have time for this).

It wouldn't be bad to check all k values for bases<=1024 for both sides. I'm not sure if I've done this.

ps. OK, checked this in gmp, there is no wrong k values in the two files.[/quote]


Robert (that is your name, correct?), please correct me if I'm wrong here:

To clarify your final statement here: Based on your testing, we definitely know that all of the conjectures given in your listings have covering sets. What we don't know is if all of the conjectures are the smallest.

Is that correct?

If so, can you suggest some parameters that we might use for covering.exe to find smaller conjectures that won't cause problems like what David (henryzz) encountered?


Gary

[quote=gd_barnes;199331]...David (henryzz)...[/quote]
[U]henry[/U]zz's name is David? :ermm:

[quote=Mini-Geek;199334][U]henry[/U]zz's name is David? :ermm:[/quote]
yes it is:smile:
my parents made me choose something not related to my name when i was young for privacy reasons:pancakebunny:
recently i have been using the name primeprover for most new accounts as it stops people calling me henry
i dont mind henryzz i am used to that but just henry bugs me:smile:

[QUOTE=gd_barnes;199331]Robert (that is your name, correct?), please correct me if I'm wrong here:

To clarify your final statement here: Based on your testing, we definitely know that all of the conjectures given in your listings have covering sets. What we don't know is if all of the conjectures are the smallest.

Is that correct?[/QUOTE]
Yes, I'm Robert.
Yes, that's correct, the given covering sets should be valid.
[QUOTE=gd_barnes;199331]
If so, can you suggest some parameters that we might use for covering.exe to find smaller conjectures that won't cause problems like what David (henryzz) encountered?


Gary[/QUOTE]

I've checked the code there should be no problem if bound_for_primes*best<2^62 is true. The promising periods are those where it has got many small divisors, like 12,24,144.

[quote=henryzz;199366]yes it is:smile:
my parents made me choose something not related to my name when i was young for privacy reasons:pancakebunny:
recently i have been using the name primeprover for most new accounts as it stops people calling me henry
i dont mind henryzz i am used to that but just henry bugs me:smile:[/quote]
bother xyxxy has read this
look at the writing under my name:glare:

[QUOTE=henryzz;199979]bother xyxxy has read this
look at the writing under my name:glare:[/QUOTE]

I think Xyzzy always does that when there is an opportunity to be annoying, but only ever when something in a post hints at that. He could put "Innumerate" under somebody's name, but he's never done it because no-one's ever hinted at it in a post. Although I don't know how Alex got "It rubs the lotion on its skin or else it takes the hose again" (which has since been removed).

[QUOTE=10metreh;200031]I think Xyzzy always does that when there is an opportunity to be annoying, but only ever when something in a post hints at that. He could put "Innumerate" under somebody's name, but he's never done it because no-one's ever hinted at it in a post. Although I don't know how Alex got "It rubs the lotion on its skin or else it takes the hose again" (which has since been removed).[/QUOTE]So far, I've got off fairly lightly.

This post is asking for trouble ...

Paul

[QUOTE=xilman;200239]So far, I've got off fairly lightly.

This post is asking for trouble ...

Paul[/QUOTE]Only just noticed the "Bamboozled" soubriquet has gone.