R96
 

Reserving R96 as new to n=25K.

There are only 298 k's remaining after the script run at n<=1K, the results are attached. Not too shabby. Going on to n=25K.

k=484 is eliminated by partial algebraic :-)

Otherwise, all matches so far. Sieved to 1e9 and ...off we go.
I'll report prelim status at 10K.

Thanks, -S

[COLOR=green]P.S. [COLOR=darkred]96 mod 97[/COLOR] for your "f generalizations", Gary! might the first one of the kind: Both k and b are -1 mod 97, so for the odd n's, divisible by 97, for evens diff.of squares.[/COLOR]

[quote=Batalov;209439]k=484 is eliminated by partial algebraic :-)

Otherwise, all matches so far. Sieved to 1e9 and ...off we go.
I'll report prelim status at 10K.

Thanks, -S

[COLOR=green]P.S. [COLOR=darkred]96 mod 97[/COLOR] for your "f generalizations", Gary! might the first one of the kind: Both k and b are -1 mod 97, so for the odd n's, divisible by 97, for evens diff.of squares.[/COLOR][/quote]

I was aware of that one and since you reserved it, I was in the process of updating the pages to show both kinds of partial algebraic factors when I saw your post here.

You are correct, I believe this is the first one where a factor of 97 combines with algebraic factors to knock out some k's; both the "new" (factor 97 on even n's) and "old" (factor 97 on odd n's) kind too.

After seeing the factorization last night as I was running it up to n=2500, if no one had taken it by Friday, I was going to take it because I was curious about it. It doesn't surprise me that it caught your interest.


Gary

[quote=Batalov;209439]k=484 is eliminated by partial algebraic :-)

Otherwise, all matches so far. Sieved to 1e9 and ...off we go.
I'll report prelim status at 10K.

Thanks, -S

[COLOR=green]P.S. [COLOR=darkred]96 mod 97[/COLOR] for your "f generalizations", Gary! might the first one of the kind: Both k and b are -1 mod 97, so for the odd n's, divisible by 97, for evens diff.of squares.[/COLOR][/quote]

Interestingly your "new" kind of algebraic factorization occurs for k=6*m^2 and m==(9 or 88 mod 97). But since k=6*9^2=486 has a trivial factor of 5 and k=6*88^2=46464 is above the conjecture, it has no effect here. All other attempts except k=484 at the "old" algebraic factorization also yield k's with trivial factors so k=484 is the only one that can be removed. The 1st posting here as well as the generalizing algebraic factors thread have now been updated.


Gary

KEP is releasing base S63. There are 237036 k's remaining at n=1K. They are too numerous to show on the pages but are available upon request.

[QUOTE]KEP is releasing base S63. There are 237036 k's remaining at n=1K. They are too numerous to show on the pages but are available upon request. [/QUOTE]

Gary, why don't you send me the file. I'll take a look at it and then make a decision on any reservation.

[quote=MyDogBuster;209651]Gary, why don't you send me the file. I'll take a look at it and then make a decision on any reservation.[/quote]

They have been Emailed. If you decide to take it on, I'd just suggest taking it up to n=5K to start with. If you do that and provide the n=1K-5K primes and k's remaining, what I'd probably do is upload a text file with the remaining k's and provide a link to it on the pages. It would be too much of a nuisance and make for way too large of a web page to list them all like base 3. I may do that anyway with the 237036 k's remaining at n=1K in case I keel over tomorrow. :-)

S60 is at n=30K, with a staggering 5 primes in a n=5K range. The primes are as follows:

123*60^26028+1
8114*60^26108+1
2007*60^26120+1
7916*60^26698+1
12140*60^29876+1

KEP!

Gary, I took a look at S63 and have decided not to reserve anything. Way too much dull and boring work. :sad:

If it had been scripted to n=2500, it would have been loads better to work with. I think the extra time for doing the script that high far outweighs the downside of having to manipulate the k ranges.

I, for one, script ALL my new bases to n=2500.

[quote=MyDogBuster;209763]Gary, I took a look at S63 and have decided not to reserve anything. Way too much dull and boring work. :sad:

If it had been scripted to n=2500, it would have been loads better to work with. I think the extra time for doing the script that high far outweighs the downside of having to manipulate the k ranges.

I, for one, script ALL my new bases to n=2500.[/quote]

I agree completely! Much easier. All of mine also go to n=2500. Here's the way I look at it: Although it takes just a little more overall CPU time than scripting to n=1000 and sieving the rest; if it takes too long to script it to n=2500 for my tastes, then I don't want to have anything to do with it for n>2500.

That said, THIS one would have taken a very long time to script to n=2500, which is why I personally would have avoided it. But hey, we do need people around who don't mind the tedium of millions of small primes so...to each his own. :-)

Thanks for your consideration and to KEP for at least getting it that far and for giving it the good old country try to get it higher before unfortunately losing it.


Gary

Reserving S35 all k's to n=25K