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