Riesel and Sierp numbers bases <= 1024

[R. Gerbicz]

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

[R. Gerbicz]

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

[Mini-Geek]

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.

[gd_barnes]

Originally Posted by Mini-Geek

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.

I think somebody should start on Riesel base 280.

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.

[henryzz]

Originally Posted by gd_barnes

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?

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

whats strange is that an exponent of 72 finds 513613045571841 but 144 doesnt
is this a bug in the covering program?

[MyDogBuster]

I think somebody should start on Riesel base 280.

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.

[Dougal]

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.

[henryzz]

144 produces

**************** Solution found ****************
482870640360662
**************** Solution found ****************
371284522956233
**************** Solution found ****************
253971311388192

288 produces

**************** Solution found ****************
203047772514813
**************** Solution found ****************
179533651185182
**************** Solution found ****************
106286297574924
**************** Solution found ****************
41294807980463
**************** Solution found ****************
31741813281359
not finished yet

120 produces

**************** Solution found ****************
367930956102524
**************** Solution found ****************
12775672337441

360 and 240 are running(walking actually)
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

[Mini-Geek]

Originally Posted by henryzz

120 produces

**************** Solution found ****************
367930956102524
**************** Solution found ****************
12775672337441

360 and 240 are running(walking actually)
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

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:

S15:  91218919470156
S280: 82035074042274
R511: 40789000085994
R15:  36370321851498
R280: 12775672337441

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.

[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.

[henryzz]

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.

based on this i have stopped my runs