I've found another case where proving a PRP will probably enable a N-1 proof. [URL]http://factorization.ath.cx/index.php?id=1100000000697059938[/URL] is a factor of (84^1087+1)/85-1.

Chris

And [url]http://factorization.ath.cx/index.php?id=1100000000697070590[/url] is a factor of (82^1279+1)/83-1 (this is more than big enough for a N-1 proof).

Chris

Both of the above are now proved (I've just clicked proof for (82^1279+1)/83). Thanks to whoever proved the factors.

Chris

Another case, 10^399*19+6*210!+1 ([url]http://factorization.ath.cx/index.php?id=1100000000706622833[/url]) N+1 has factor (10^399*19+6*210!+2)/41681226 ([url]http://factorization.ath.cx/index.php?id=1100000000706656405[/url]) which is a PRP. It only appeared in the list of PRPs after I clicked on N+1 for 10^399*19+6*210!+1.

Chris

[URL="http://factordb.com/index.php?id=1100000000708833005"](200^277+1)/201[/URL]
[URL="http://factordb.com/index.php?id=1100000000708833215"](378^277+1)/379[/URL]
[URL="http://factordb.com/index.php?id=1100000000708829776"](161^331+1)/162[/URL]
[URL="http://factordb.com/index.php?id=1100000000708840082"](230^313+1)/231[/URL]
[URL="http://factordb.com/index.php?id=1100000000708829573"](249^317+1)/250[/URL]

There are a bunch more [URL="http://factordb.com/listtype.php?t=1&mindig=747&perpage=100&start=0"]starting at 747 digits[/URL].

Going through them I found two cases where proving a PRP will enable a N-1 proof of a larger prime:
[url]http://factorization.ath.cx/index.php?id=1100000000708875224[/url] ((803^653+1)/804 needs [url]http://factorization.ath.cx/index.php?id=1100000000708897053[/url] ((803^326+1)/644810).

[url]http://factorization.ath.cx/index.php?id=1100000000708875229[/url] ((964^743+1)/965) needs [url]http://factorization.ath.cx/index.php?id=1100000000708909223[/url].

Chris

Another case, proving [url]http://factorization.ath.cx/index.php?id=1100000000718032814[/url] will probably enable [url]http://factorization.ath.cx/index.php?id=1100000000717857598[/url], (2^9550-7)/9, to be proved prime.

Chris

The first has been proved, so I've just proved (2^9550-7)/9 is prime. Thanks to whoever provided the certificate (Factordb says it was uploaded by Anonymous).

Chris

I did it with the latest version of Primo. Happy to help :)

And proving [url]http://factorization.ath.cx/index.php?id=1100000000739094598[/url] will probably enable a N+1 proof for [url]http://factorization.ath.cx/index.php?id=1100000000739040138[/url] (136^1300+135).

Chris

Another case, proving [url]http://factorization.ath.cx/index.php?id=1100000000750837630[/url] (((10^416+10^208+1)*(2^689-3)/3+10^624*486+1)/2^208/12286671) will enable a N+1 proof for [url]http://factorization.ath.cx/index.php?id=1100000000748438039[/url] ((10^416+10^208+1)*(2^689-3)/3+10^624*486).

Chris