[QUOTE=firejuggler;342595](and sorry Puzzle-Peter, i snatched this one from you)[/QUOTE]

That's fine. They're only a few minutes of work each. But I must admit I was wondering about some of my certificates not being needed when I uploaded them.

[URL="http://factordb.com/index.php?query=38502*529^38502-1"]38502*529^38502-1[/URL] ;-)

My first tiny GW prime. (Outside of FactorDB, it is proven of course.)

PRP list had [URL="http://factordb.com/index.php?query=10^338*4%2B10^169*6%2B3"]10^338*4+10^169*6+3[/URL]

It's obviously 4x^2+6x+3, and P-1 factors as (2x+1)*(x+1)

I see other large PRPs from forms like this, but there are cofactors after removing small divisors, so the algebra doesn't work.

Spotted [URL="(311^898+1)/96722"](311^898+1)/96722[/URL] in the PRP list today. The denominator is 311^2, so P-1 is (311^896-1). Helping factordb find the algebraic factors enabled the proof.

Found [URL="http://factordb.com/index.php?id=1100000000208003131"](2^9053+7)/39[/URL] in the PRP list. Adding the algebraic factors of (2^9048-1) enabled the N-1 proof.

Also [URL="http://factordb.com/index.php?id=1100000000349887759"](2^9066*67-1)/267[/URL], which needed algebraic factors from 2^9064-1 to enable the N-1 proof.

And [URL="http://factordb.com/index.php?id=1100000000291757645"](10^2731*7-67)/3[/URL]

And [URL="http://factordb.com/index.php?id=1100000000439186999"](828^937-1)/827[/URL]

And [URL="http://factordb.com/index.php?id=1100000000208003206"](2^9099+7)/15[/URL]

[URL="http://factordb.com/index.php?id=1100000000593916950"]10^2739+10^297-1[/URL] already had all the N+1 factors. All I did was press the proof button.

[URL="http://factordb.com/index.php?id=1100000000315305495"](2^9109*7+1)/15[/URL]

I factored (5189^303+1)/(5189^101+1).
That enabled the N-1 proof of (5189^607-1)/5188.

[URL="http://factorization.ath.cx/index.php?id=1100000000294458842"]2^13645-511[/URL][SUB]<4108>[/SUB] was waiting for someone to click on the "Proof" button (N-1), I did it.

(10^6439*8-791)/9 also waited for a click (by N-1).

(I've found it in M.Kamada's primesize.txt list; and after that checked that Phi[SUB]6437[/SUB](10) has had a certificate since 2008. Factordb also had it on record.)

I factored 252^473-1.
That enabled the N-1 proof of (252^947-1)/251.

I'm doing a lot of these.

(2^27721*57-1)/113 and (2^27721*55-1)/109 needed the known factors (2^27720-1) added to the N-1. Fortunately doing the first automatically spilled over into the second.

Factoring the remaining [URL="http://www.factordb.com/index.php?id=1100000000636547508"]C109[/URL] in [URL="http://www.factordb.com/index.php?id=1100000000020330335"]2097^63-1[/URL] enabled the N-1 proof of [URL="http://www.factordb.com/index.php?id=1100000000439187032"](2097^757-1)/2096[/URL]
The proofs of the following ones were enabled by adding algebraic factors to N-1 or N+1
[URL="http://www.factordb.com/index.php?id=1100000000294468641"]2^8451-9[/URL] => N+1
[URL="http://www.factordb.com/index.php?id=1100000000371050988"](2^8461*91-1)/181[/URL] => N-1
[URL="http://www.factordb.com/index.php?id=1100000000630630692"](2^8465+3)/35 [/URL]=> N-1