How 'bout this? [URL="http://factordb.com/index.php?query=2837%21%5E2%2B2837%21%2B1"]2837!^2+2837!+1[/URL] (a.k.a. Phi(3,2837!) )

This one will be a bit harder (will need some more factoring and a CHG on it) - [URL="http://factordb.com/index.php?query=%282415%21%5E5-1%29%2F%282415%21-1%29"]Phi(5,2415!)[/URL]

These extend [URL="https://oeis.org/A051856"]A051856[/URL] and [URL="https://oeis.org/A200906"]A200906[/URL]

[QUOTE=Batalov;279671]How 'bout this? [URL="http://factordb.com/index.php?query=2837%21%5E2%2B2837%21%2B1"]2837!^2+2837!+1[/URL] (a.k.a. Phi(3,2837!)[/QUOTE]

How'd ya do dat? Factordb says it has an N-1 proof, but N-1 shows no known factors.

Well, in the same way as [URL="http://factordb.com/index.php?query=6001%21%5E2%2B6001%21%2B1"]Phi(3,6001!)[/URL] :-]

(just submitted it to a worker for a PRP test -- and the FactorDB apparently finds all 6001! factors one by one because it takes an inordinate amount of time, but when it does, it realizes that N-1 with the next prime is in order)

Spotted [URL="http://factordb.com/index.php?id=1100000000031611272"](10^1296*13-7)/123[/URL] in the PRP list. Applying the algebraic factors to N-1 was not quite enough to prove it prime, but a few clicks on the scan button provided the one more needed factor.

Another cute one [URL="http://factordb.com/index.php?id=1100000000315170611"](2^5367*7+1)/57[/URL] was proven by N-1 method.

<Taking a break for the night.>

Edit: [URL="http://factordb.com/index.php?id=1100000000004709927"](10^1621*77-41)/729[/URL] by N-1.

[QUOTE=RichD;279900]Another cute one [URL="http://factordb.com/index.php?id=1100000000315170611"](2^5367*7+1)/57[/URL] was proven by N-1 method.

<Taking a break for the night.>

Edit: [URL="http://factordb.com/index.php?id=1100000000004709927"](10^1621*77-41)/729[/URL] by N-1.[/QUOTE]
Well, in the same way as [URL="http://factordb.com/index.php?query=7606%21%5E2%2B7606%21%2B1"]Phi(3,7606!)[/URL] :-]


<Taking a break for the night.>

[URL="http://factordb.com/index.php?query=7076%21%5E2%2B7076%21%2B1"]Phi(3,7076!)[/URL] :-] in fact...

[URL="http://factorization.ath.cx/index.php?id=1100000000291680537"](10^1365*88-97)/9[/URL] by N+1 by adding the algebraic factors of 10^1365-1

[URL="http://factordb.com/index.php?id=1100000000001167959"](5^2498+1)/26[/URL] is proven prime by applying the algebraic factors of 5^2496-1 to N-1.

[URL="http://factordb.com/index.php?id=1100000000349578791"](191*2^6105-1)/381[/URL] is proven prime by applying the algebraic factors of 2^6104-1 to N-1.

[URL="http://factordb.com/index.php?id=1100000000005327544"](10^1900+3)/7[/URL] is proven prime by applying the algebraic factors of 10^1899+1 to N+1.

[QUOTE=Batalov;279952][URL="http://factordb.com/index.php?query=7076%21%5E2%2B7076%21%2B1"]Phi(3,7076!)[/URL] :-] in fact...[/QUOTE]

then ...