[I PMed a moreorlessidentical draft of this to Prime95, ATH; yorix, jasonp, philmoore and R. Gerbicz yesterday]
F25F30 cofactor status:
In the context of testing the cofactorPRP functionality which will be supported in Mlucas v21, I've at long last done Suyamastyle PRP tests on the cofactors of F25F30, using the Pépintest residues I've generated for same over the past 10 years, as detailed in this thread  original primalitytests for F2526 detailed in post #1 (recently updated with latest results), F27 in #2 and #5, F28 in #4 and #20, F29 in #29,#42,#52. For F30, the interimresidue files and logfile for the completed run @60 M FFT have been uploaded but the 99.5%complete doublecheck run @FFT 64M is stalled due to my KNL having gone offline last week  I suspect the cheapie PSU installed by the vendor of this barebones system, but not yet had time to get under the hood, so to speak.
The cofactorPRP results are tabulated in a "Part 2" followup to this note. My code only supports the Suyama cofactorPRP method, which starts from the basic Pépintest residue, does one modsquaring to generate the FermatPRP residue A from that and an additional lg2(F) modsquarings to generate the subtrahend B for the Suyama test, where F is the product of known prime factors; it makes little sense to spend roughly the same amount on a direct PRP test of such cofactors as needed by the Pépin test of F_m, only to have to redo a similar amount of work when a new factor is discovered.
I first added some basic cofactorPRP code to Mlucas in early 2018, and used it to test the cofactors of F2529 using the Pépintest residues I had generated via my primaiity tests for same. Did not post the cofactorPRP results at the time because the accompanying Res64 values mismatched ones posted by Andreas Höglund (a.k.a. ATH), who had done cofactorPRP tests of F25 and F26 using George's code. At the time I was trying to figure out why said result mismatched Andreas' value for what I thought was the same quantity, and in the ensuing PM exchange it did emerge that George's codeatthetime (2009) which Andreas used in fact was doing a directPRPtest of the cofactor, but I was unaware of the cofactorPRP runs for F25 and F26 done by forumite Yar (a.k.a. yorix  details below) in late 2017 using the thenlatest Prime95 version. Having more pressing concerns at the time I decided to put that aside and revisit later. Mlucas v21 will have 2 major feature adds, PRPCF and PRPcert support, so in the context of the first, 'later' is now.
In 20092010 Andreas Höglund used George's code to test the cofactors of F2527; cf. Posts #51, #62, #64 in
this thread:
Quote:
UID: athath, F25/known_factors is not prime. RES64: 44BFC8D231602007. Wd1: B9307E03,00000000
Known factors used for PRP test were: 25991531462657,204393464266227713,2170072644496392193
UID: athath, F26/76861124116481 is not prime. RES64: 6C433D4E3CC9522E.
UID: athath, F27/151413703311361/231292694251438081 is not prime. RES64: 481F26965DE16117.

Those posts were not clear on precisely what *type* of cofactorPRP test was run  direct FermatPRP test on the cofactor C, or a Pépintest (R = 3^((N1)/2) (mod N)) of the Fermat number N = F*C followed by the Suyama postprocessing step (cf. the post by Phil Moore
here), where one computes first the FermatPRP residue A = 3^(N1) (mod N) = R^2 (mod N) via a single modsquaring of the Pépintest residue R, then uses the product of known factors F to compute B = 3^(F1) (mod N), and checks if the difference (A  B) is divisible by the cofactor C. The Suyama version is preferable because it starts with a basic Pépintest of the N, and as new factors are found that same residue can be used to quickly (#of squarings = bits in productofknownprimefactors) check each resulting cofactor for PRPness.
In late 2017 user Yar (don't know last name, uid = yorix)
posted a thread about his own cofactorPRP runs for F2526, again using George's code, but now mentioning 2 different run types for each, which clarifies the types of cofactorPRP tests used:
Quote:
PRP test for F25 with known factors: PRP=N/A,1,2,33554432,1,"25991531462657,204393464266227713,2170072644496392193" gives 'composite' with res64: 7B6B087B84A45562
PRP test for F26 with known factors: PRP=N/A,1,2,67108864,1,"76861124116481" gives 'composite' with res64: FBB406B3A281838C

We see that Res64 differs from ATH's above  Yar notes "This test with base 3 and returns the same residue independent of the number of known factors", which indicates a Suyamastyle cofactorPRP test.
For F25 and F26 my FermatPRP Res64 values match Yar's for the Suyamastyle cofactor check, and his directcofactor results match ATH's (though that is a samesoftwareused match). But it would be nice if someone using George's code could confirm not just the FermatPRP residues (A) for the above, but for purposes of pronouncing the ensuing cofactorPRP results "crossverified using independent codes", we should also crosscheck the (A  B) mod C ones, where C is the cofactor. The FermatPRP computation of course constitutes the overwhelming bulk of a PRPCF run, but it is important to also have assurance that the Bresidue and (A  B) mod C have been correctly computed.
[
@George, would it be possible for you to tweak your code to print the Res64 checksum for the latter quantity? If Yar still has the FermatPRPtest residues from his runs of F25 and F26 using your code, it would then be a simple matter to rerun the Suyama step from those and crosscheck the (A  B) mod C residues. If not, the F25 and F26 fulllength tests are now easily runnable on modest hardware.
Also, is there a different Prime95/mprime worktodoentry syntax for a directPRP test of a cofactor vs a 2step approach (FermatPRP of N = F*C followed by Suyama step, or did you switch from the former to the latter along the way? Yar only echoes the workfile entry for the 2step run, but notes that used 29.4 and then in a later post notes retrying with v29.3 and getting results matching Andreas' earlier ones.
]
Lastly, I did not see any post by Yar regarding a Suyamastyle cofactorPRP test for F27 using Prime95. It would be nice for someone to do such so we can put that one to bed, as well, at least until another factor is discovered. I could obviously do it myself, but I think the "different persons using different codes" optics would be better. Compute cost would be 2030% more than a current GIMPS wavefrontPRP test.
Results for my Mlucas v21prototype cofactorPRP runs follow in Part 2.