[QUOTE=henryzz;291469]What have people checked from the numbers I posted? I can check some more tomorrow.[/QUOTE]
I have proven many of the numbers you've posted.

Not many in the last file, yet.

(11^1724*5+1)/6-1 need help with (11^431*3+3)/1516829834365402334277715308 or (11^862*3+3)/992082412380769750967560817656886431636998
(10^1627*14+13)/603+1 need (10^1625*25+11)/4141336702683390924663927819 factors
(10^1631*14-41)/99-1 need help with either(10^815+1)/(10^163+1) or(10^815-1)/(10^163-1)
(2^5358*175-1)/111-1) need help with (2^2677*5+1)/23300488449386234700116099
((2^5434*135+1)/79+1) need help with (2^1810*3+1)/1115755075968493924957
(2^5440*177+1)/591329-1 is FF but has a PRP1615 (proded, no luck)
((10^1731-1)*911/999+10^1731)/273-1 is FF but has a PRP1715(proded, no luck)
((10^1742*5+31)/1262187+1)/6534662+1 is FF, PRP1725 (proded, no luck)
((10^1841*79-7)/340407-1)/233854+1 is FF PRP1825 (proded, no luck)

and I poked a number of other (mainly 8-20 digits prime)

[B]Test finished![/B]
[B]PFGW output:[/B]

Primality testing (11^2577-1)/(11^859-1)/133 [N-1, Brillhart-Lehmer-Selfridge]
Prime_Testing_Warning, unused factor from helper file: 61 Prime_Testing_Warning, unused factor from helper file: 826129 Running N-1 test using base 7
Calling Brillhart-Lehmer-Selfridge with factored part 33.44% (11^2577-1)/(11^859-1)/133 is prime! (0.2408s+0.0001s)Proven by combined N+1/N-1-method

Henry,

I think the provable primes from your lists have been proven. But I see there are still easy pickings for higher numbers. I jacked the digit count up and scanned less than 200 PRPs before spotting [URL="http://factorization.ath.cx/index.php?id=1100000000315350692"](2^10069*19+1)/39[/URL]. Are you going to extend your search to higher PRPs?

And just below it was [URL="http://factorization.ath.cx/index.php?id=1100000000291740572"](10^3031*35-359)/9[/URL]

[QUOTE=wblipp;291808]I think the provable primes from your lists have been proven.[/QUOTE]

Double checking, I found some in the first list that could still be completed. I believe these really are as complete as possible with algebraic factors and the known factordb results. I haven't double checked the other lists yet.

Some 3 for 1 opportunities gleaned from Henry's Post #75. A Primo proof of the first number will enable a N+/-1 proof of the second number which will enable an N+/-1 proof of the third number.

[URL="http://factorization.ath.cx/index.php?id=1100000000491664220"](((2^6616*11-1)/35+1)/18978-1)/218489095992628142393749204529429310[/URL]
[URL="http://factorization.ath.cx/index.php?id=1100000000378751554"]((2^6616*11-1)/35+1)/18978[/URL]
[URL="http://factorization.ath.cx/index.php?id=1100000000362737724"](2^6616*11-1)/35[/URL]

[URL="http://factorization.ath.cx/index.php?id=1100000000460876206"](((10^1841*79-7)/340407-1)/233854+1)/12767374[/URL]
[URL="http://factorization.ath.cx/index.php?id=1100000000426709209"]((10^1841*79-7)/340407-1)/233854[/URL]
[URL="http://factorization.ath.cx/index.php?id=1100000000000756898"](10^1841*79-7)/340407[/URL]

[URL="http://factorization.ath.cx/index.php?id=1100000000441718576"](((10^1742*5+31)/1262187+1)/6534662+1)/423806[/URL]
[URL="http://factorization.ath.cx/index.php?id=1100000000426685941"]((10^1742*5+31)/1262187+1)/6534662[/URL]
[URL="http://factorization.ath.cx/index.php?id=1100000000000811390"](10^1742*5+31)/1262187[/URL]


This came from the same source, but I cannot find a third prime in the chain:
[URL="http://factorization.ath.cx/index.php?id=1100000000438688459"](((10^1731-1)*911/999+10^1731)/273-1)/107767440900618[/URL]
[URL="http://factorization.ath.cx/index.php?id=1100000000412150747"]((10^1731-1)*911/999+10^1731)/273[/URL]

Edwin Hall uploaded a certificate for a prp1139 that emerged from (9636^1093-1)/9635-1. This allowed me to prove a p4351.

I've been adding several such numbers lately. The one closest to a proof is (5995^1009-1)/5994. N-1 is 32.79% factored.

I don't think these are proven before, since the [base]>[5*the exponent].

[QUOTE=lorgix;291896]The one closest to a proof is (5995^1009-1)/5994. N-1 is 32.79% factored.
[/QUOTE]
Use Konyagin-Pomerance test with >30% factored, and the C-H-G method all the way down to 26.0% (and a bit below).

The fun part is doing Konyagin-Pomerance test from scratch. The PN-ACP book has its description, it's short and sweet. Or you can get existing recipes from the yahoo primeform discussion group - but this is less fun.

I might search higher digits. Downloading the numbers in pages of 1000 gets tedious quickly.
If someone provides me with the list of prps then I can put virtually any amount through my program.

factordb can give you the entire list of prp, if you click the right link...

[QUOTE=firejuggler;292038]factordb can give you the entire list of prp, if you click the right link...[/QUOTE]
Whoops!! Didn't reallize it was in downloads. Will do it now.