Other primes thread

[gd_barnes]

Originally Posted by MyDogBuster

Thanks Gary.

So basically, if I find a prime with a k divisible by 3, I could test for a twin but probably won't find one. Can't hurt though. I may even find one.

You betcha!

My suggestion would be to take a group of Riesel primes where k's are divisible by 3 and sieve them using srsieve for the Proth form up to some low limit. Usually the sieve will eliminate either all of them or all but a few of them.

To avoid redundant checking, for anything k<1200, stick to n>260K because I've already checked up to n=260K. For higher k's, which our 8th/9th/10th drives have plenty of primes for now, you could start at n=48K. That is as high as I've gotten in my testing of all k<1M.

Come to think of it, an excellent starting point would be the n=50K-200K portion of our 9th drive. 80% of the k's are > 1200 and all n are > 48K. That would be by far the most effective place to start because we already have the primes sorted nicely by k-value. After that, continuing with the n=200K-350K portion of that drive would be good because all k's are > 1200. There you go!

Any twin for n>~80K makes the top-20 list at top-5000 and is reportable! I have one for n=100K with a 10-digit k.


Gary

[MyDogBuster]

Just a side note. On my independent work, I just submitted 9615*2^991347-1. A nice juicy one. 298430 digits.

My largest prime ever.

[gd_barnes]

Way to go! A nice one! We've been missing the really big ones lately.

[Brucifer]

Originally Posted by MyDogBuster

Just a side note. On my independent work, I just submitted 9615*2^991347-1. A nice juicy one. 298430 digits.

My largest prime ever.

A nice one indeed Ian!

[gd_barnes]

One thing I forgot to mention: That one was PrimeSearch/NPLB's largest prime also!

[MyDogBuster]

One thing I forgot to mention: That one was PrimeSearch/NPLB's largest prime also!

Does that mean I get a bonus on my next check? LOL

[kar_bon]

Originally Posted by MyDogBuster

Does that mean I get a bonus on my next check? LOL

... the next 'check' of a candidate? YESSSSSSSS!

[Mini-Geek]

Originally Posted by gd_barnes

Come to think of it, an excellent starting point would be the n=50K-200K portion of our 9th drive. 80% of the k's are > 1200 and all n are > 48K. That would be by far the most effective place to start because we already have the primes sorted nicely by k-value. After that, continuing with the n=200K-350K portion of that drive would be good because all k's are > 1200. There you go!

Is there any good way to take the list of primes and sieve their +1 sides? I put it all in a spreadsheet to to eliminate the excess info (who found it, etc.), eliminate non-0 mod 3 candidates, and change it to +1. This gives a file with lines like "1005*2^149604+1". I just put it into PFGW with the -f option (to factor 'em first). (at about k=1500, or half of the way, already!) Is there a better way to easily get such a list into a proper sieving program? (I probably won't have time to use it instead for this check of drive 9, but if we're going to do more, as discussed over in this thread, it'd be nice to know)
I'll post or edit this when I finish so everyone can know that the drive 9 primes have been checked for twins...
Edit: I just realized I eliminated n != 0 mod 3, instead of k != 0 mod 3. Restarting...Edit 2: Included the n=200K-350K primes from drive 9, too.

[Mini-Geek]

Originally Posted by Mini-Geek

Is there any good way to take the list of primes and sieve their +1 sides? I put it all in a spreadsheet to to eliminate the excess info (who found it, etc.), eliminate non-0 mod 3 candidates, and change it to +1. This gives a file with lines like "1005*2^149604+1". I just put it into PFGW with the -f option (to factor 'em first). (at about k=1500, or half of the way, already!) Is there a better way to easily get such a list into a proper sieving program? (I probably won't have time to use it instead for this check of drive 9, but if we're going to do more, as discussed over in this thread, it'd be nice to know)

I was able to get it into an ABCD format (or NewPGen or anything else), so sr2sieve can sieve it starting at 1995 (the largest k) but couldn't find a good way to get it sieved up to there...
Any suggestions? SRsieve (I've got 0.6.9) is crashing when printing lines like this: "removed candidate sequence 1137*2^n+1 from the sieve", so that isn't working right to get the sieve started.
Edit: Never mind, updated my srsieve and it finished to 1e6 without a problem.

[Mini-Geek]

Done, no primes.

[gd_barnes]

Interesting. I had already done most of what you did 2 years ago for the top 5000 primes at that time. It took me quite a while and involved a lot of manual work. I encountered some of the same problems that you did so I had to resort to running multiple instances of srsieve or doing tests individually. It's nice to know that sr(x)sieve can handle multiple different forms where a k gets completely eliminated due to small factors now with the more recent releases. I seem to remember that the problem happened when there was just 1-2 primes of a specific k and the sieve eliminated all of them. It happened sometimes but not all of the time.

If you're really bold, you could try testing for twins on the entire top-5000 database including the as of now, primes that are no longer top 5000. Due to the manual effort involved, I only did about 60-70% of the top 5000 at that time and none of the non-top-5000 at the time. You could even tweak your script or whatever to test for Sophie-Germains (SGs) or their Sierp equivalent; I can't remember what the latter are called. That would be cool if you found something. SGs have the exact same chance of occurring as twins but are not nearly as popular for searching so it takes a much lower one to make the top 20.

One thing to keep in mind on twins that helped me out that perhaps you already thought of: The k must be divisible by 3. Before sieving, I put the primes in a spreadsheet, parsed out the k-value, put a column in for the k-value mod 3, and eliminated all k's where the 2nd column was not a 0. That helped me eliminate a fair percentage of them without even testing. Something similar may apply to SGs.

Edit: I also took lists of primes from Karsten's pages. That's another source that you could use. I remember finding an n=~10K twin for k=915, although it wasn't big enough to make the top 20 twins at the time, which required an exponent of n=~66K. There are likely many primes on his lists that never made top 5000, especially for some of the huge k's that the RPS folks tested way-back-when, that would be big enough to make the top 20 if they turned out to be twin or SG.


Gary