9791642389174771^13-1
C183

factors as:

[CODE]r1=3947850070017072334399246099826412197445240766520376140072461844640401702117158804852441 (pp88)
r2=92341198769365423983250627830940980861148443692905891465180106885045159439306187154329129792511 (pp95)[/CODE]

5081095716541357^13-1
C189

factors as:

[CODE]r1=2813482530268402146261235323322875440766951389329703294996306287754418370395866482901 (pp85)
r2=105255376899928662843235099360764538265756380196011007851400210157731359827549087159056179478466924203201 (pp105)[/CODE]

15881^47-1 factors as: [code]
r1=398899378847338760982357219445758192131351 (pp42)
r2=43605863609910601912851449289412480503978170215731371189917262293278600358379696006281655371300280524949569792789085816803978964458063026950907607713377 (pp152)
[/code]
Which should have been found by ECM. Does anyone know how much ECM has been run against numbers in the "most difficult" list on Pascal's site?

Chris

A half-brilliant result for 17761^47-1
r1=3939356233545045976948700173749675582738460495931987 (pp52)
r2=844427860206691631431771576331528244729242936591288305315271289545786249 (pp72)
r3=898540589706321487473061647646510983508054809355407936562117068053178989 (pp72)

Two of the factors being the same length and leading digit.

Chris

329473262366294657316493043899400715093065093^5-1
C176

Factors as:

[CODE]r1=59066439250364916029837100887036578644075148783403732240679131 (pp62)
r2=262153256730983793994994009124416961426982157191241762365466205842138014922810496589717241591471714087494081249711 (pp114)[/CODE]

10453074620347880113528227943613^7-1
C170

factors as:

[CODE]r1=250263639693603463801025922770431355613747303909395755792705887959 (pp66)
r2=14357499195899139535066451963667077989175123854379926977006609552882198883372040818337004176361872945281 (pp104)[/CODE]

8970971^29-1
C178

factors as:

[CODE]r1=70264364422828967075134718033861996334050325254836378198320360027278781637 (pp74)
r2=36725343251735454979631612552647177066911313100767350008173964467430370894651791358027745040687621291279 (pp104)[/CODE]

Needed 55M relations instead of the ~34M predicted.

9235379541700294893241592533312191410548921^5-1
C159

factors as:
[CODE]r1=20596779392232538867397744474415813750227442143502270853031057319887959841 (pp74)
r2=10688563222648484311033929319138862297052955920216104716923660966488935232253341820121 (pp86)[/CODE]

18813315461^19-1
C172

factors as:
[CODE]prp60 factor: 410204858804842761201351975616485855135224022324114825822623
prp112 factor: 8158692262322557694170734699002391908857904663695009062903449586746310909934689912628379616676436409287052985237[/CODE]

I've factored 3 similar numbers from the most wanted list and I expected them to take similar times. But:
26737^37-1 took 12:32:46
26783^37-1 took 07:42:39
27481^37-1 took 04:56:06

Which surprised me. Especially since the smallest number took longest. So I checked how msieve rated them:
26737^37-1 skew 0.18, size 1.276e-08, alpha 2.260, combined = 8.506e-11 rroots = 2
26783^37-1 skew 0.18, size 2.092e-08, alpha 0.519, combined = 1.205e-10 rroots = 2
27481^37-1 skew 0.18, size 4.293e-08, alpha -2.166, combined = 1.998e-10 rroots = 2

The E-scores vary more than I would expect for similar polys. And the alpha scores vary a lot which looks interesting.

Can I assume the varying times are mainly due to varying alpha?

Chris

The alpha score is a lottery ticket, for SNFS you are stuck with it but for GNFS you can tweak the polynomial to greatly improve alpha. Yes, the better alpha score means that sieve values for the third problem are smaller than sieve values for the first problem by a factor of about e^4.4