Sierp base 43 complete to n=25K; 2 k's remain

Sierp base 55 complete to n=25K; 7 k's remain

Sierp base 68 complete to n=25K; 2 k's remain


See details on the web pages.

Sierp bases 50, 54, 56, 59, 62, and 65 were easily proven and have now been added to the web pages.

[quote=Flatlander;161475]Sierp base 42 tested to 15,000.
50 ks remaining.[/quote]


k=1, 42, & 1764 make GFNs and so are not considered. This removes k=42 from your remaining list meaning that only 49 k's remain.

k's that are powers of Sierp bases can be immediately removed just like k's with trivial factors. This only has an effect on even bases.

< 5 mins. testing showed that the only prime for 42^n+1 is at n=1 in a test run up to n=2^16-1 (n=65535). Therefore, k=42 is primeless to n=32767 and k=1764 is primeless to n=16383 and hence are unlikely to ever yield primes.


Gary

[quote=gd_barnes;162332]k=1, 42, & 1764 make GFNs and so are not considered. This removes k=42 from your remaining list meaning that only 49 k's remain.

k's that are powers of Sierp bases can be immediately removed just like k's with trivial factors. This only has an effect on even bases.

...
Gary[/quote]
Sorry, I looked for base^2 but forgot about base^1 and base^0.

Sierp bases 69, 74, 76, and 77 were all easily proven.

Sierp base 53 is complete to n=9K. 40 k's remain.
Sierp base 57 is complete to n=10K. 3 k's remain.
Sierp base 72 is complete to n=6K. 6 k's remain.

Continuing on all to n=25K.

All info. is shown on the web pages.

The only thing that I have remaining to update the CRUS pages for is Chris's Riesel base 39 effort and Micha's Riesel base 3 effort for k=560M-570M.

If anyone sees anything that I have missed, please let me know.


Gary

Per Chris's testing a while back, I have now updated the web pages to show 14,894 k's remaining on Riesel base 39 at n=1000. I thought some of you might be humored to see so many numbers on one page so [URL="http://gbarnes017.googlepages.com/Riesel-conjecture-base39-reserve.htm"]here[/URL] it is. At 120 KB, it's larger than the entire Riesel conjecture reservations page for all bases and nearly 3 times as large as the Sierp conjecture reservations page for all bases!

After spending 2-3 hours to remove algebraic factors, verifying correct inclusion/exclusion of multiples of the base, confirming that all k's were accounted for, formatting them in a manner for displaying on the page, and doing a double-check to make sure that the count was accurate, this lead me to the following conclusion:

If you want your k's remaining shown on the pages, there should be < 10,000 k's remaining. If there are more, I'm sorry, you'll just have to test the base some more. (lol)

I had told Chris that I would be fine showing as many as 100,000 k's remaining on a base but after going through that ordeal, I changed my mind. :smile:


Gary

Thanks for all that Gary. :smile:

I won't be testing Riesel base 40 btw !!!

[quote=Flatlander;162419]Thanks for all that Gary. :smile:

I won't be testing Riesel base 40 btw !!![/quote]


Oh, darn. How disappointing!

Besides, there is a better alternative: Sierp base 71.

With a conjecture of k=~5.9G, I think you and KEP should tackle that one and see if you can get it down to < 10,000 k's remaining. Good luck with that! :missingteeth:

Of course there's always Riesel or Sierp base 910. With a conjecture of P=~5T on both sides, it should keep you entertained for a while.

But then there is Riesel base 280. That should be really fun! See if you can get that down to < 10,000 k's remaining. With a conjecture of k=~513.6T, over 1000 times greater than either side of base 3, the fun there might be to write a program that can come up with a smaller k that has a covering set.

Can you say lots of small primes? BORING!


:smile: Gary

Taking Riesel base 58

Riesel Base 58
 

63677*58^10082-1
7814*58^10165-1

Riesel Base 58
 

49428*58^10244-1
66888*58^10266-1
105303*58^10366-1
9066*58^10394-1