factordb uses PFGW, which only supports the 1/3 method of proof. I think Rogue currently maintains PFGW - perhaps he could be persuaded to add one of the lower factorization methods if somebody with deep enough understanding was willing to work with him.

[URL="http://factordb.com/index.php?id=1100000000322070941"](2^10263*9+1)/73[/URL] N-1

[URL="http://www.factordb.com/index.php?id=1100000000647393071"](2^2349-3)/67[/URL] N-1
[URL="http://www.factordb.com/index.php?id=1100000000647393570"](2^3031-3)/5[/URL] N-1 & N+1 both fully factored

I have attached a load of numbers that all convert to the form 2^n+-1
I would be interested to see how many you can prove.

all those below (2^13367*7+1)/27 are proven. Don't know if it is by cert or autommatically (there is some below 300 digits).
(2^13367*7+1)/27 proved by +1

[QUOTE=henryzz;369284]I have attached a load of numbers that all convert to the form 2^n+-1
I would be interested to see how many you can prove.[/QUOTE]
I think the following are the only non-trivial ones that don't have a +/--proof yet. Some only need a primality proof for a large cofactor of p+1 or p-1.

[CODE](3*2^2577+1)/11
(9*2^3253+1)/17
(3*2^4055+1)/5
(3*2^4959+1)/5
(9*2^5813+1)/17
(3*2^6592+1)/7
(9*2^11853+1)/17
(3*2^17939+1)/5
(7*2^18357+1)/15
(3*2^18411+1)/5
(3*2^18638+1)/13
(5*2^19294+1)/9
(9*2^26637+1)/17
(5*2^35672+1)/21
(5*2^35990+1)/21
(5*2^36442+1)/9
(11*2^38042+1)/45
(7*2^38559+1)/57
(5*2^38612+1)/21
(3*2^42634+1)/49
(3*2^51376+1)/7
(9*2^51637+1)/17
(5*2^52381+1)/11
(3*2^52786+1)/7
(3*2^56488+1)/7
(3*2^61870+1)/49
(11*2^62306+1)/45
(3*2^67930+1)/7
(3*2^70129+1)/7
(3*2^78999+1)/5
(9*2^81853+1)/17
(5*2^82112+1)/21
(3*2^83978+1)/13
(7*2^87577+1)/15
(3*2^93851+1)/5
(5*2^94768+1)/9[/CODE]

I have seen at least one where the cofactor was 2-PRP(as are all cofactors of 2^n+1 I think) but was composite.

(145^145-7)/6 proved by n+1 (I only had to click the prove button). I then noticed that a certificate had been submitted by RobertS but not processed. Sorry for treading on your toes Robert.

Does the certificate exploit N+1 or n-1? If not it would be worth checking for cases like this before generating the certificate (but that might be hard to automate).

Chris

The Primo certificate format only allows for a Pocklington N-1 or BLS75 theorem 15 N+1 test. These are quite useful for pushing the N size down, but aren't usually sufficient to work by themselves for the size numbers we're looking at.

The verifier understands a different format that can do BLS75 theorem 3 (improvement over Pocklington) and theorem 5 proofs at any step. This isn't currently allowed in FactorDB, as it only accepts Primo certificates.

I've thought that adding the N+1 method BLS75 theorem 17 to the verifier and to my prover would be nice, as would the combined method BLS75 Corollary 11 (with a reasonable bound for B to keep the verification time down).

[URL="http://factordb.com/index.php?id=1100000000671295396"](10^308*5+10^231*4+10^154*3+10^77*2+1)/3 [/URL] adding the (x+1) factor allowed an N-1 proof

I've just had a look at the list of primality certificates that are waiting to be processed and noticed several for (expression)+1 or (expression)-1. They could be proved faster with N-1 or N+1. I decided not to do that myself though.

Most of the ones like that I noticed were submitted by RKN ChristianB

There is quite a backlog because factordb hasn't had as many helpers to process certificates running as usual. At present there's only 1 and it seems to be stuck on something.

Chris