[QUOTE=FactorEyes;131885]More natural whole-number goodness:[/QUOTE]
I'll see if I can post updated web tables later today. I'll be on vacation for the next 2 weeks so there will be no further updates until mid-May.


Paul

[QUOTE=xilman;131896]I'll see if I can post updated web tables later today. I'll be on vacation for the next 2 weeks so there will be no further updates until mid-May.[/QUOTE]Posted a few minutes ago. Under 300 composites now remaining.


Paul

I was going back through old messages in this thread, and came across these dealing with SNFS factorization of 6^247 + 5^247.

[quote=FactorEyes;104146]
Currently dead in the water on 6,5,247+. Built 5 matrices, with lower and lower weights, only to see the sqrt fail every time. I knew that the ggnfs sqrt dislikes sextics, but not this much. I may go straight at this one with a quintic.

[/quote]

[quote=frmky;104156]
[code]N <number>
R0 -22452257707354557240087211123792674816
R1 3552713678800500929355621337890625
A0 6
A1 0
A2 0
A3 0
A4 0
A5 5
A6 5

FRMAX 8200000
FAMAX 8200000

[/code]

Greg[/quote]

I can't figure out how Greg arrived the quoted poly, which gnfs complains does not have a common root...

Also why the factor of 13 in the exponent wasn't used... to whit:
[code]
[SIZE=2]c6: 1[/SIZE]
[SIZE=2]c5: -1[/SIZE]
[SIZE=2]c4: -5[/SIZE]
[SIZE=2]c3: 4[/SIZE]
[SIZE=2]c2: 6[/SIZE]
[SIZE=2]c1: -3[/SIZE]
[SIZE=2]c0: -1[/SIZE]
[SIZE=2]Y1: -11622614670000000000000000000[/SIZE]
[SIZE=2]Y0: 371683090626368450957356181641[/SIZE]
[/code]

where the linear poly is (6^19*5^19)*x - (6^38 + 5^38).

The latter would seem to be the best polynomial for this and other exponents containing factors of 11 or 13, right?

- ben.

[QUOTE=bsquared;132883]
I can't figure out how Greg arrived the quoted poly, which gnfs complains

The latter would seem to be the best polynomial for this and other exponents containing factors of 11 or 13, right?
[/QUOTE]
Note the comment "filling in the appropriate poly and fb limits." The quoted poly was just to show the format, not to actually run anything. :smile: Also, yes, use the factor of 13.

Greg

[quote=frmky;132975]Note the comment "filling in the appropriate poly and fb limits." The quoted poly was just to show the format, not to actually run anything. :smile: Also, yes, use the factor of 13.

Greg[/quote]

Boy, I wish I'd have read that comment before banging my head against a wall for a not-insignificant amount of time... :redface:

Thanks for the clarification.

I've spent some time on these numbers since work on 3^512+1 stopped, and in light of this post from another thread...

[quote=xilman;132892]
...
Once I've caught up from post-vacational trauma (over 21K spam emails flushed today alone!) ...
Paul
[/quote]

... I assume that one or more results emails may have gotten lost.

Here's a list o' SNFS fun from the last week:

[code]
11^197-7^197 =
prp65 factor: 20708792194081369162343887660130414484596077984291075456883990707
prp69 factor: 246933304980719833462486098708298319084664255080023774824779868024079

10^185-9^185 =
prp51 factor: 105181130360135100082275673478205701894313783514991
prp91 factor: 1600068784023350592649493277394210048321964231867858108261646864849854315294318463559747201

11^149-8^149 =
prp72 factor: 178911293478493719631230906006771565467380378721993936092038555827152393
prp74 factor: 61514549101942224765288621083676445585385535122135509782420512238930754603

12^151-7^151 =
prp60 factor: 145936421575862770067132478580496418017661633517079386226263
prp100 factor: 8202948624637490689911909255473359239000342340536492357902139014873301603966245238287216835305456693

11^157-10^157 =
prp47 factor: 39070798286321847069927565552136955618031865561
prp117 factor: 806861786250139413545822778007277365481857577765022882297393626586291348965403308687444568817668603042800565828465011

11^163-2^163 =
prp50 factor: 51742438637162348422260175905516291342699691565941
prp120 factor: 119927361252254990869770636340709970211172284793004587954635953530491904932855193421386648950371630362914340092451844367

12^163-11^163 =
prp80 factor: 34957698771189765331782973598371343662802452976654329112913699889505994900648923
prp97 factor: 2306747025295127756657870419577411038780260831935613811132503821954020694612281320931385429666039

11^173-6^173 =
prp40 factor: 3955280409902443377746127828603267824773
prp66 factor: 189120982836804146945957179752676847736263650891407830423655954643
prp68 factor: 11480658697661329720039669320896268226480245406049180145845552955337

11^179-5^179 =
prp86 factor: 15543044572549874019621852807031176787177758644778330893265283024862436243881386329029
prp89 factor: 82009066601789258759566764211610026991016297148212173179950504818404751088731468276541223

12^179-7^179 =
prp55 factor: 3613920779994003706635360865067593492177579857842600581
prp65 factor: 54469336545566164708492283496811303344649495251159691087390406809
prp71 factor: 10570514689677093394713198774724035567340078327492430846285016639478433

10^151+3^151 =
prp47 factor: 28432674708414087532908554873622133270694787517
prp80 factor: 25800190772816108951186457374172726600355737094590236364403359157012258634609327

11^191-5^191 =
prp54 factor: 319881748965585144111273816136535126576888398148894429
prp143 factor: 10956286468150935403301608279368360408731943729330015014758177161076664732613719572966291291343369366181392132918587629071052849339788740927283

12^161+5^161 =
prp44 factor: 17362919919788941854322191916060381233410273
prp100 factor: 2304748378576246555642007188222340875156466108974091334807892815532066746561008477972979246087319277

By GNFS
11^151+10^151 =
prp45 factor: 177961660759146339515290326119447932037203163
prp70 factor: 2549798574742323678052352172546462492297490037201739863867663224066289


[/code]

[QUOTE=bsquared;132992]... I assume that one or more results emails may have gotten lost.[/QUOTE]Nope. I've just not had time yet. It may be the weekend before an update is posted.

Paul

This just finished:

[code]
5^293 - 3^293 factors as

prp87 factor: 112490476684505410879269692505113821845501106695036524579494994589055369291870479478747
prp119 factor: 27929651561546840428782945757881830405289188029898651944978475216791998566125669033809043868812344068884161357368300083
[/code]

[QUOTE=xilman;133015]Nope. I've just not had time yet. It may be the weekend before an update is posted.

Paul[/QUOTE]An update has just been posted. There are 34 new factors this time and the number of remaining composites has fallen to 265.

I'd love to be proved wrong but I suspect that it will be quite a while before the tables need extending again.


Paul

[QUOTE=xilman;133236]I'd love to be proved wrong ...
[/QUOTE]
I'm not sure whether these should be a screaming priority. I'm not asserting that they shouldn't, as is obvious from the amount of processor time I have thrown at them, but I really don't know one way or another.

I assume that they're just about as important as conventional Cunningham numbers, because projective varieties and homogeneity are all around, so it seems natural to extend any investigation to the projective case.

I guess I'm asking if there's a concrete justification for factoring these, other than (a) they're pretty neat, and (b) they're obvious SNFS targets.

BTW, is there a limit to the size of A, in A^k +/- B^k, beyond which the algebraic norms get too big, or the root structure of the polynomials get's too weird, causing SNFS to bog down?

[QUOTE=FactorEyes;133249]

I assume that they're just about as important as conventional Cunningham numbers, because projective varieties and homogeneity are all around, so it seems natural to extend any investigation to the projective case.

[/QUOTE]

They are not nearly as important from either a
mathematical or an historical point of view.

[QUOTE]


I guess I'm asking if there's a concrete justification for factoring these, other than (a) they're pretty neat, and (b) they're obvious SNFS targets.

BTW, is there a limit to the size of A, in A^k +/- B^k, beyond which the algebraic norms get too big, or the root structure of the polynomials get's too weird, causing SNFS to bog down?[/QUOTE]

I started these tables. Why? Because I needed a convenient set of
relatively small numbers to test my twiddlings with my NFS code. The
smallest candidates in the Cunningham and Fibonacci tables had grown
to big to be test cases. People who did not have extensive NFS
experience wanted to learn how to use NFS without having to tackle
very large numbers, so I made the tables public and suggested their
availability.

There are not any limits on A,B, except practical computing limits.