The probable primes - Page 32

Batalov · 2012-10-22, 20:46

It could be a factor for some other number, and as such its character has to be known. Here's where it sits. It is an extremely useful data warehouse. Their internal validation is different from Primo, an open-source script (there was a discussion some place in the factordb thread).

Here's some fun that you can have with this now proven number P=2^56366+39079:
If you construct a PRP of a form a*(P^3+b*P^2+c*P)+-1 (that's only for example; you can use some other forms), then you can immediately prove it prime by N+-1 method based on P being a proven prime.

Cybertronic · 2012-10-22, 21:00

Wow Peter , congratulations !

Dubslow · 2012-10-22, 21:15

Quote:

Originally Posted by Puzzle-Peter

Thanks!

Factordb? I think I've read this before but honestly I don't even really know what it is. I can guess from the name though. But this numbers does not have any factors. I am confused. I think I need to do some reading...

Quote:

Originally Posted by Batalov

It could be a factor for some other number, and as such its character has to be known. Here's where it sits. It is an extremely useful data warehouse. Their internal validation is different from Primo, an open-source script (there was a discussion some place in the factordb thread).

Here's some fun that you can have with this now proven number P=2^56366+39079:
If you construct a PRP of a form a*(P^3+b*P^2+c*P)+-1 (that's only for example; you can use some other forms), then you can immediately prove it prime by N+-1 method based on P being a proven prime.

Nominally after a certificate has been uploaded the status changes from PRP to P, but c.f. here, that's broken at the moment. Pretend it's a P.

Batalov · 2012-10-22, 21:41

Quote:

Originally Posted by Dubslow

Nominally after a certificate has been uploaded the status changes from PRP to P, but c.f. here, that's broken at the moment. Pretend it's a P.

Nothing is broken. You've never dealt with primes large enough. There's always a delay for the validation step. It is surely infinitesimal for PRPs of the aliquot run-of-the mill size.

I had submitted sizeable certificates before. For them, the delay is significant. Now, here, this particular number is a monster. Nothing will be "usual" here. Not only FactorDB, but the UTM pipeline will be quite possibly manually shunted. (UTM makes special notes for offsite validations that they cannot reproduce but that had come from trusted sources.)

P.S. Ho-ho-ho. Look at out old "friend" Liquid N₂. Submitted a PRP to them instead of Lifchitz&Lifchitz. It will be removed - look at it now before too late.

philmoore · 2012-10-22, 22:19

Congratulations! At 16968 digits, it is the fourth largest prime proven by ECPP, and the largest proven by Marcel Martin's Primo.

Puzzle-Peter · 2012-10-23, 14:41

Quote:

Originally Posted by Batalov

Nothing is broken. You've never dealt with primes large enough. There's always a delay for the validation step. It is surely infinitesimal for PRPs of the aliquot run-of-the mill size.

I had submitted sizeable certificates before. For them, the delay is significant. Now, here, this particular number is a monster.

Is validating the same as re-running Phase2 in PRIMO? That took one week with 16 threads on 12 physical cores.

Batalov · 2012-10-23, 18:04

No, it is much faster. It verifies that all relations are valid. (There's also a very fast signature checking, that's almost instantaneous, but only checks that the file is not damaged in transfer or not manually edited.)

It should be done today. (Running on a slow 4-cpu box.) ...Done. The certificate is valid.

Puzzle-Peter · 2012-10-26, 06:22

I see a user comment has been added on Chris Caldwells pages. Thanks! Could anybody tell me how to do this in the future? I can edit the existing comment now which is great because the sendspace link will expire and I hope to see the certificate an Marcel Martins page at some point (no answer to my email to him yet). But how can I make a new comment? I seem to be unable to find out

Batalov · 2012-10-26, 06:56

David is your co-author; I guess that is an authentication worth enough.
Log in with the credentials you created (PrimeGrid for example could create an account for you that you won't be able to log in to, but here, this is not the case), and look around.

I've never had an occasion to post a comment. Standard official comments had been posted on my behalf, e.g. a Generalized Fermat note. If I will happen to find a Proth prime that will be a Generalized Fermat Factor, PrimeGrid will compute that and also post it on my behalf.

Puzzle-Peter · 2012-12-14, 12:58

Quote:

Originally Posted by Batalov

David is your co-author; I guess that is an authentication worth enough.

Does that give me a non-infinite Erdős number?

certainly the closest I'll ever get.

However, here's a little pre-christmas present:

2^61792+21661 is now a certified prime.

http://www.sendspace.com/file/0tt6t5

Cybertronic · 2012-12-14, 18:06

Only german.

Hallo Peter, herzlichen Glückwunsch ! Das nenne ich mal eine Hausnummer ... dagegen erscheint mein Rekord von 2010 ein Witz zu sein.

Gruß

Norman

2012-10-22, 20:46	#342
Batalov "Serge" Mar 2008 San Diego, Calif. 3²×7×163 Posts	It could be a factor for some other number, and as such its character has to be known. Here's where it sits. It is an extremely useful data warehouse. Their internal validation is different from Primo, an open-source script (there was a discussion some place in the factordb thread). Here's some fun that you can have with this now proven number P=2^56366+39079: If you construct a PRP of a form a(P^3+bP^2+cP)+-1 (that's only for example; you can use some other forms), then you can immediately prove it prime by N+-1 method based on P being a proven prime. Last fiddled with by Batalov on 2012-10-22 at 20:56*

2012-10-23, 18:04	#348
Batalov "Serge" Mar 2008 San Diego, Calif. 3²·7·163 Posts	No, it is much faster. It verifies that all relations are valid. (There's also a very fast signature checking, that's almost instantaneous, but only checks that the file is not damaged in transfer or not manually edited.) It should be done today. (Running on a slow 4-cpu box.) ...Done. The certificate is valid. Last fiddled with by Batalov on 2012-10-24 at 02:25

2012-10-26, 06:22	#349
Puzzle-Peter Jun 2009 700₁₀ Posts	I see a user comment has been added on Chris Caldwells pages. Thanks! Could anybody tell me how to do this in the future? I can edit the existing comment now which is great because the sendspace link will expire and I hope to see the certificate an Marcel Martins page at some point (no answer to my email to him yet). But how can I make a new comment? I seem to be unable to find out Last fiddled with by Puzzle-Peter on 2012-10-26 at 06:23

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2012-10-22, 21:00	#343
Cybertronic Jan 2007 Germany 3×239 Posts	Wow Peter , congratulations !

2012-10-22, 22:19	#346
philmoore "Phil" Sep 2002 Tracktown, U.S.A. 19×59 Posts	Congratulations! At 16968 digits, it is the fourth largest prime proven by ECPP, and the largest proven by Marcel Martin's Primo.

2012-10-26, 06:56	#350
Batalov "Serge" Mar 2008 San Diego, Calif. 281D₁₆ Posts	David is your co-author; I guess that is an authentication worth enough. Log in with the credentials you created (PrimeGrid for example could create an account for you that you won't be able to log in to, but here, this is not the case), and look around. I've never had an occasion to post a comment. Standard official comments had been posted on my behalf, e.g. a Generalized Fermat note. If I will happen to find a Proth prime that will be a Generalized Fermat Factor, PrimeGrid will compute that and also post it on my behalf.

2012-12-14, 18:06	#352
Cybertronic Jan 2007 Germany 3·239 Posts	Only german. Hallo Peter, herzlichen Glückwunsch ! Das nenne ich mal eine Hausnummer ... dagegen erscheint mein Rekord von 2010 ein Witz zu sein. Gruß Norman