Thanks to Vollnoob/yoyo@home

3602407438103418087310110702859943140744217508967 | (7^431-1)

[QUOTE=Pascal Ochem;205687]___sigma(P122^4) = [COLOR="Green"]32491 * 37366575223151 * (C468)[/COLOR] /* 613^70 * P122^4 * C486 is greater than 10^1000 */[/QUOTE]Not sure about the sigma, found on curve 26 by Dario's ECM applet.

i currently have 4.5M relations for sigma(293459^28):smile:

[QUOTE=Pascal Ochem;202671][url]http://www.lri.fr/~ochem/opn/t1000.txt[/url]

tXXX.txt contains composite numbers encountered
when targetting the lower bound 10^XXX.

If you factor one of them, then the proof-tree will be reduced,
and this factorization will not become useless
because of the factorization of some other number.
[/QUOTE]sigma(11723974435124342185539834025169127024124352188895164878195757^2):[code]prp38 factor: 10857366606905840358225000151537123033
prp43 factor: 2761575257115619656105173691517100442403567[/code]sigma(38934969278521^16):[code]prp41 factor: 83224255739379586424497038366163715339851
prp44 factor: 29773297806977911058930101452726297288502789[/code]

A small factor found several times by yoyo@home

572749682520506652634407616247 | 7^439-1

William

sigma(55371657433379061738079^6):[code]prp31 factor: 1228728457349763496938179933209
prp60 factor: 419077405983008079619714876617687144426796150788124324778671[/code]
sigma(6874631660053183220120526370954314535267799520287653^2):[code]prp40 factor: 5302241178618924012797449029670361159269
prp53 factor: 11823514028956487995125993715930146939884138260888207[/code]
sigma(12534219388905427^12):[code]prp41 factor: 16079028802508806360597360112432996348897
prp52 factor: 4359977845598272757076518581118691539852489438400131[/code]
sigma(15614588321448160999912954257996576487^4):[code]prp39 factor: 394195289742058203090683354451809986091
prp54 factor: 189674308622743649252166369123068442669405539669108401[/code]
sigma(102981794654323063^6):[code]prp35 factor: 27762284591442799203011261063869841
prp58 factor: 3424036427484398470564656764208556075938138849587251139041[/code]

From [url]http://www.lri.fr/~ochem/opn/t500.txt[/url]

sigma(7017607616783^12)
[CODE]prp44 factor: 10357173108483254145287782661752763314998289
prp53 factor: 50908513988982228353188115111902851562735646626916171
[/CODE]

I'm relatively new to SNFS, and I tried to set up the C96 from sigma(15008538895398688503343773594490169791961^4)

as
[CODE]n: 691444975898687300216454107724428198521123464293057407877880737581968128534060302970644797536881
m: 15008538895398688503343773594490169791961
c0: -1
c5: 1
type: snfs
skew: 1
[/CODE]

But I'm getting no relations

[CODE]-> This is client 1 of 1
-> Using 2 threads
-> Working with NAME=sigma-15008538895398688503343773594490169791961-4...
-> SNFS_DIFFICULTY is about 200.882.
-> Selected default factorization parameters for 200.882 digit level.
-> Selected lattice siever: ggnfs_64/gnfs-lasieve4I14e
-> Creating param file to detect parameter changes...
-> Q0=7800000, QSTEP=100000.
-> makeJobFile(): q0=7800000, q1=7900000.
-> makeJobFile(): Adjusted to q0=7800000, q1=7900000.
-> Lattice sieving rational q-values from q=7800000 to 7900000.
=> "ggnfs_64/gnfs-lasieve4I14e" -k -o /tmp/sigma-15008538895398688503343773594490169791961-4.spairs.out.T1 -v -n0 -r sigma-15008538895398688503343773594490169791961-4.job.T1
=> "ggnfs_64/gnfs-lasieve4I14e" -k -o /tmp/sigma-15008538895398688503343773594490169791961-4.spairs.out.T2 -v -n0 -r sigma-15008538895398688503343773594490169791961-4.job.T2
FBsize 2013661+0 (deg 5), 527152+0 (deg 1)
FBsize 2013661+0 (deg 5), 527152+0 (deg 1)
total yield: 0, q=7891493 (inf sec/rel)
[/CODE]

I'm going to switch back to GNFS for this one, but I'd like to know if I'm just confused and doing it wrong.

[quote=apocalypse;206136]...I'm going to switch back to GNFS for this one, but I'd like to know if I'm just confused and doing it wrong.[/quote]
No, just change the "c5/c0" part to
[code]c4: 1
c3: 1
c2: 1
c1: 1
c0: 1[/code]
(The poly must not be reducible to m.)

[COLOR=blue]EDIT: I haven't looked how small the number was (a c96). Continue with GNFS, it will be in fact faster.[/COLOR]

Thanks!

sigma(15008538895398688503343773594490169791961^4)
[CODE]prp48 factor: 119927803464035534849376686836269929496374393671
prp49 factor: 5765510214702137785827719909551844853594889701511[/CODE]

Question for Pascal about the tXXX.txt files:

Have the numbers had ECM run to a particular depth? Is it worth running ECM on them or are they all ready for sieving now?

I didn't know if anyone else would find this useful - most folks here seem to be well-versed in setting up the NFS factoring - but I wrote a (long) perl one-liner to help me choose which of S/GNFS to run on the numbers in Pascal's tXXX.txt files, and I thought I'd share it.

[CODE]perl -ane 'chomp($F[2]); $c = length($F[2]); $d = log($F[0])/log(10) * (1 + $F[1]); if ($F[1]%4 != 0 && $F[1]%5 != 0 && $F[1]%6 != 0) { $d = log($F[0])/log(10) * (2 + $F[1]);} $d = int($d + 0.5); $g = int($d / 1.4 + 0.5); $t = "GNFS"; if ($c > $g) { $t = "SNFS"; } print "sigma($F[0]^$F[1]) C$c, D$d, G$g, $t\n";' t500.txt [/CODE]

sample output (Cxx is the length of the composite, Dxxx is the SNFS difficulty, and Gxxx is the GNFS comparable difficulty = Dxxx / 1.4)
[CODE]
sigma(69710210289691^12) C97, D180, G129, GNFS
sigma(5502997992185822133325044025114218231630382402194049024447^2) C97, D231, G165, GNFS
sigma(172919530897^16) C99, D191, G136, GNFS
...
sigma(600803554877143^10) C119, D163, G116, SNFS
sigma(926659^30) C119, D185, G132, GNFS
sigma(1501489387^16) C119, D156, G111, SNFS
...
[/CODE]

The script assumes that if some i in {4,5,6} divides the exponent, the polynomial will be ax[SUP]i[/SUP]-1, and otherwise x[SUP]j[/SUP]-a for some j in {4,5,6}, which might not be optimal, but seemed good enough for a first pass.

The D/G ratio of 1.4 was chosen based on a few forum posts I found, but could well be wrong.

I welcome any suggestions.

I'm currently working on
sigma(1009^58) C164, D180, G129, SNFS
with m=1009^12, poly=x[SUP]5[/SUP]-1009