Bases 33-100 reservations/statuses/primes

[mdettweiler]

Originally Posted by gd_barnes

Oh, that's easy. It's just faster to use Alptertron's site. lol

36*73^1 = 2628 == (1 mod 37)
36*73^2 = 191844 == (36 mod 37)
36*73^3 = 14004612 == (1 mod 37)
36*73^4 = 1022336676 == (36 mod 37)
[etc.]

Now, when you subtract 1 from the above, you get (0 mod 37) for the odd n's. :-)

I don't believe it's a true proof in the classical sense of the word, but it demonstrates conclusively that all odd n are divisible by 37.

BTW, I'm pretty sure I got Alpertron's site to work on one of my Linux machines. I'll check it when I get home. But...I thought you had a Windows machine also.


Gary

Ah, I see now.

As for Alpertron's site on Linux machines: the main problem on my machine in particular is that I think something might be broken on the backend that's causing errors whenever I try to set up the Java browser plugin in Firefox. As you said, I did have a Windows virtual machine set up that I could use, but it seems that an upgrade of the virtualization software broke that too... (I blame Windows for requiring a reinstall due to the virtual "IDE controller" having changed ever-so-slightly...but I guess the VirtualBox people could have put in some sort of compatibility mode pretty easily if they wanted to. )

However, I just found that under Linux I can use PARI/GP (a handy-dandy freeware math application that can do all sorts of stuff) to factor these numbers at least as easily as with Alpertron's applet.

[Flatlander]

Just for fun, I also tested Riesel base 94, k=29 to 20,000. Results attached. (No sieve file. No reservation. Stopping there.)

[gd_barnes]

Originally Posted by Flatlander

Just for fun, I also tested Riesel base 94, k=29 to 20,000. Results attached. (No sieve file. No reservation. Stopping there.)

Thanks for the nice sieve file. I'm compiling a list of things to do while on a business trip for doing when I get back next Tuesday. I'll make sure I get the sieve file posted to the web pages after getting them updated for all of these bases.

I think I've stuck a chord here...easier to prove bases. I may continue doing this for the Sierp side as well as for some bases > 125. Proving bases is fun! :-)


Gary

[Flatlander]

How many of the 19 ks for Reisel base 87 would you 'expect' to fall before n=20,000?

[Flatlander]

Originally Posted by Flatlander

How many of the 19 ks for Reisel base 87 would you 'expect' to fall before n=20,000?

In other words, I've already started testing this base to n=20,000.

[Siemelink]

Originally Posted by Flatlander

How many of the 19 ks for Reisel base 87 would you 'expect' to fall before n=20,000?

I'd guess 3.

Willem.

[Flatlander]

Originally Posted by gd_barnes

...
There is a thread that has all of the conjectured values for all bases on both sides up to 1024...
Gary

Can someone post a link to these values please.

[KEP]

http://robert.gerbicz.googlepages.com/sierpinski.txt
http://robert.gerbicz.googlepages.com/riesel.txt

Hope this helps!

KEP

[gd_barnes]

Originally Posted by Siemelink

I'd guess 3.

Willem.

I would concur with that. I'd say it's slightly more likely that you'll get 4 primes than 2 primes so an expection of a bit more than 3. For info. purposes, here are the top 10 primes that I found up to n=10K that gives a general idea of how they have fallen:

1128*87^3171-1
1002*87^3257-1
1398*87^3699-1
1426*87^3778-1
1284*87^4444-1
1186*87^5151-1
102*87^5508-1
1586*87^6195-1
628*87^6371-1
508*87^9016-1

This is another one of those highly misleading bases. It is unlikely to be proven in several hundred CPU years; believe it or not! :-) Except for highly prime bases, any base that is not a power-of-2 that has more than 10 k's remaining at n=10K will be virtually impossible to prove anytime in the near future and for most of them, not likely in most of our lifetimes without new concepts or math on finding primes; even taking into account increases in computer speeds.

So far, we've only had 2 bases proven with conjectures > 1000...Sierp bases 11 at k=1490 and 21 at k=1002. But we have two bases with only one k remaining that would shatter those records: Sierp base 9 and 10. Proving Sierp base 10 would be a great coupe! With a conjecture of k=9175, it would be an outstanding proof! :-)


Gary

[gd_barnes]

I have added and udpated search limits and reservations to the original post about these bases 50-100. I will continue doing so until I get my web pages updated with all of the info.

Let me know if you see any problems.


Gary

[Flatlander]

Originally Posted by KEP

http://robert.gerbicz.googlepages.com/sierpinski.txt
http://robert.gerbicz.googlepages.com/riesel.txt

Hope this helps!

KEP

Thanks for the links Kenneth! Just what I was looking for. When Gary's got 5 minutes I'm sure he'll add all this to his website. lol

I have tested Riesel Base 87 to 20,000. Three primes were found, good estimates guys!
Verified primes:
758*87^13638-1
898*87^14455-1
958*87^17047-1

(Though Gary suggested there should be 3-and-a-bit primes, and I can't find the bit...)

I have also sieved a file to p=560bn, n=100k. I estimate that this is sufficient to test further to about n=28,000. (Hopefully by then another prime will have been found making further sieving faster.)

Unreserving this er, conjecture.


edit:
My estimate above is based on the fact that tests at n=20,000 took one minute and the sieve was rejecting candidates about every two minutes; 28^2 is about twice 20^2.

edit2:
The exact sieve depth is 560973747863