[URL="http://factorization.ath.cx/index.php?id=1100000000212781985"]5426!/2713!/2713!+1[/URL] needed some help finding the gazillion tiny factors of N-1.

i.e.

[URL="http://factordb.com/index.php?id=1100000000225099082"]3^3298*2-5[/URL] needed help finding the algebraic factors of 3^3297-1 for the N-1 proof. The big P881 revealed in the algebraic factors was proven by Primo Certificate by klajok on July 26th.

[URL="http://factorization.ath.cx/index.php?id=1100000000294664800"]40^883-39[/URL] needed help finding the algebraic factors of 40^882-1 to complete the N-1 proof.

[URL="http://factorization.ath.cx/index.php?id=1100000000237280068"](2^4518-3)/253[/URL]

N-1 is (2^4518-256)/253 = 256*(2^4810-1)/256.

Factordb needed help seeing the algebraic factors of 2^4801-1.

polcyclo(10,n!) are nice -- their N-1 has factors from n!, n!-1

101!^4-101!^3+101!^2-101!+1
107!^4-107!^3+107!^2-107!+1
267!^4-267!^3+267!^2-267!+1
316!^4-316!^3+316!^2-316!+1

Nudged n!-1 factors into the fDB, now it's time to wait for the small ones to "prove themselves", ...and maybe run C-HG for larger ones.

P.S. polcyclo(15,n!) may need a bit of help, e.g. [URL="http://www.factordb.com/index.php?id=1100000000467529955"]134!^8+134!^5+134!^3+1-134!^7-134!^4-134![/URL] :-)

I've been finding it harder to spot candidates in the PRP list that just need help with algebraic factors and the scan button. This is partly because the list has been picked over, and partly because, with the current wavefront of Primo Proofs in the 1300 digit range, it's rarer for "scan" to be enough help. Today, though, I spotted

[URL="http://factorization.ath.cx/index.php?id=1100000000294465047"]2^4441+17[/URL]

The N-1 includes 2^4437+1, and the algebraic factor 2^(4437/3)+1 had been missed.

Today I found [URL="http://factorization.ath.cx/index.php?id=1100000000291689055"]10^1595-100001[/URL] in the PRP list. N+1 was missing the 10^(1590/3)-1 algebraic factor.

Oh. In this case, there must be a trove of similar known proven primes at M.Kamada's [URL="http://homepage2.nifty.com/m_kamada/math/primesize.zip"]site[/URL]. They are just not in the factorDB.

Tonight I spotted [URL="http://factorization.ath.cx/index.php?id=1100000000349328658"](2^4537*53-1)/105[/URL] in the PRPs. The factordb didn't know that N-1 had algebraic factors in common with 2^4536-1

Near the leading edge of Primo proofs I found, [URL="http://factorization.ath.cx/index.php?id=1100000000294465164"]2^4557+9[/URL]. N-1 needed the algebraic factors of 2^4554+1. I was surprised such an obvious example was still available.