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Old 2010-05-07, 11:58   #1
Mini-Geek
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Default no twin left behind?

I was just thinking about this again:
http://www.mersenneforum.org/showthread.php?t=12591 (looking for twin primes by searching the 'other side', i.e. swapping -1 and +1, of a known prime)
But the top 5000 list has so many different prime forms, and is only accessible through text or HTML (both of which would not be terribly easy to extract the essentials from) it'd be non-trivial to get a list of candidates to test. So then I thought of NPLB: tons of primes, all in the form k*2^n-1, all in a central DB that can pick out the k and n for me. Easy!
I'd like to apply this idea to the full list of NPLB primes. NPLB has found 6604 (as of this writing) primes for -1, and I'd like to find if any of those have a twin on the +1 side. I could try to download all the pages and extract the k and n, but I figured it'd be easier to ask one of you with DB access to dump the list for me. (consider it requested preferably in the NewPGen format of one "k n" per line)
6604 candidates of all sizes before any sieving is sure to reduce to a handful of testable candidates. TBH I'm not too hopeful that such a twin does exist, but it'd be such an easy check it's almost a waste to look for new primes to find their twins before checking old primes to see if they have twins.

Last fiddled with by Mini-Geek on 2010-05-07 at 12:26
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Old 2010-05-07, 13:24   #2
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You can also obtain an even greater list from my RieselPrimeDatabase for download here!

I've just updated this list (and the twins-list, too). It's in the npg-format sorted by n-values for all primes in all summary-pages.

Last fiddled with by kar_bon on 2010-05-07 at 13:24
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Old 2010-05-07, 13:55   #3
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stupid mouse failure lol (using mousekeys).

(10:46) gp > for(n=1,10,for(k=1,10,if(isprime(k*2^n-1) && isprime(k*2^n+1),print(k"*"2"^"n"+ or -1"))))
2*2^1+ or -1
3*2^1+ or -1
6*2^1+ or -1
9*2^1+ or -1
1*2^2+ or -1
3*2^2+ or -1
9*2^3+ or -1
6*2^5+ or -1
3*2^6+ or -1
9*2^7+ or -1
(10:46) gp >

this what you want ?
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Old 2010-05-07, 14:54   #4
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Quote:
Originally Posted by science_man_88 View Post
this what you want ?
No, I think not!

Those small twins are all known (see list at download or the summary-pages).

He was asking of higher n-levels say n~500000 for any prime of the form k*2^n-1.
Test those k/n-pairs if the number k*2^n+1 is prime, too! The Riesel-side (-1) is known to be prime for many values here but none has ever tested the '+1'-side!
OTOH the chance for finding a new twin by testing only these primes is very low.

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Old 2010-05-07, 15:12   #5
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Quote:
Originally Posted by Mini-Geek View Post
I was just thinking about this again:
http://www.mersenneforum.org/showthread.php?t=12591 (looking for twin primes by searching the 'other side', i.e. swapping -1 and +1, of a known prime)
But the top 5000 list has so many different prime forms, and is only accessible through text or HTML (both of which would not be terribly easy to extract the essentials from) it'd be non-trivial to get a list of candidates to test. So then I thought of NPLB: tons of primes, all in the form k*2^n-1, all in a central DB that can pick out the k and n for me. Easy!
I'd like to apply this idea to the full list of NPLB primes. NPLB has found 6604 (as of this writing) primes for -1, and I'd like to find if any of those have a twin on the +1 side. I could try to download all the pages and extract the k and n, but I figured it'd be easier to ask one of you with DB access to dump the list for me. (consider it requested preferably in the NewPGen format of one "k n" per line)
6604 candidates of all sizes before any sieving is sure to reduce to a handful of testable candidates. TBH I'm not too hopeful that such a twin does exist, but it'd be such an easy check it's almost a waste to look for new primes to find their twins before checking old primes to see if they have twins.
If you want I can dump the DB's list for you rather easily, but it sounds like Karsten's list might be even better, since it contains ALL known Riesel primes rather than just NPLB's. If you'd still like to get the DB's list, though, let me know.
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Old 2010-05-07, 15:34   #6
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Quote:
Originally Posted by kar_bon View Post
No, I think not!

Those small twins are all known (see list at download or the summary-pages).

He was asking of higher n-levels say n~500000 for any prime of the form k*2^n-1.
Test those k/n-pairs if the number k*2^n+1 is prime, too! The Riesel-side (-1) is known to be prime for many values here but none has ever tested the '+1'-side!
OTOH the chance for finding a new twin by testing only these primes is very low.
I am annoyed by mousekeys and it may take hours for my pari code to do this if I could use message boxes in win32 assembly good I'd try that.

the hard part is a prime check loop I think if I use Iczelion's win32 ASM tutorials. I did buy a ASM book though but it's for HLA might have to adapt it to win32, or someone else can try this as I suck at it lol.

Last fiddled with by science_man_88 on 2010-05-07 at 15:47
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Old 2010-05-07, 15:47   #7
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Quote:
Originally Posted by science_man_88 View Post
I am annoyed by mousekeys and it may take hours for my pari code to do this if I could use message boxes in win32 assembly good I'd try that.
If you don't mind my asking, why bother using MouseKeys in the first place (since if it's that annoying, I'm assuming you don't need it for accessibility reasons)?
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Old 2010-05-07, 15:50   #8
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Quote:
Originally Posted by mdettweiler View Post
If you don't mind my asking, why bother using MouseKeys in the first place (since if it's that annoying, I'm assuming you don't need it for accessibility reasons)?
I'm using mousekeys because my mouse stopped working so outside of speech it's the only way I know to have a way to click thinks.
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Old 2010-05-07, 15:53   #9
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Quote:
Originally Posted by kar_bon View Post
You can also obtain an even greater list from my RieselPrimeDatabase for download here!

I've just updated this list (and the twins-list, too). It's in the npg-format sorted by n-values for all primes in all summary-pages.
That should work great, thanks. I'll see if I can find any twins that aren't already known.
Quote:
Originally Posted by science_man_88 View Post
this what you want ?
No, what Karsten said.
Quote:
Originally Posted by mdettweiler View Post
If you want I can dump the DB's list for you rather easily, but it sounds like Karsten's list might be even better, since it contains ALL known Riesel primes rather than just NPLB's. If you'd still like to get the DB's list, though, let me know.
Unless for some reason there're any primes in the DB but not in Karsten's list, no I don't need NPLB's list. Thanks anyway.
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Old 2010-05-07, 17:55   #10
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Status update: I'm currently at n=119k. I've found a decent number of twins that aren't in Karsten's list, but the largest is only 42932385 832 (42932385*2^832-1 and +1 for FactorDB entries), which at 259 digits is not even close to making any notable twin prime lists. I'll send the full list of total and new twins when I'm done checking all numbers.

Last fiddled with by Mini-Geek on 2010-05-07 at 17:59
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Old 2010-05-07, 18:00   #11
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Quote:
Originally Posted by Mini-Geek View Post
I've found a decent number of twins that aren't in your list, but the largest is only 42932385 832 (...) I'll send the full list of total and new twins when I'm done checking all numbers.
Good job! So I can eliminate some missings/errors from my database then!
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