Riesel and Sierp numbers bases <= 1024

[gd_barnes]

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.

[Mini-Geek]

Originally Posted by gd_barnes

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.

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.

[henryzz]

Originally Posted by Mini-Geek

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.

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

[R. Gerbicz]

Originally Posted by gd_barnes

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.

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:

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)

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)).

[gd_barnes]

Originally Posted by R. Gerbicz

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.

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

[Mini-Geek]

Originally Posted by gd_barnes

...David (henryzz)...

henryzz's name is David?

[henryzz]

Originally Posted by Mini-Geek

henryzz's name is David?

yes it is
my parents made me choose something not related to my name when i was young for privacy reasons
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

[R. Gerbicz]

Originally Posted by gd_barnes

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?

Yes, I'm Robert.
Yes, that's correct, the given covering sets should be valid.

Originally Posted by gd_barnes

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

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.

[henryzz]

Originally Posted by henryzz

yes it is
my parents made me choose something not related to my name when i was young for privacy reasons
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

bother xyxxy has read this
look at the writing under my name

[10metreh]

Originally Posted by henryzz

bother xyxxy has read this
look at the writing under my name

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).

[xilman]

Originally Posted by 10metreh

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).

So far, I've got off fairly lightly.

This post is asking for trouble ...

Paul