Contribution and Reservation

(38·10²⁰¹-11)/9 =: 4(2)₂₀₀1_<202>; = 3⁷ · 7 · 17 · 41 · 67 · 683 · 344959 · 3300678041_<10> · 3393625603793_<13> · 473441739439981307524197101_<27> · [4726774286751842953544764096924572983754513684930460331886785876580852931325969539457794460735815378513837608100859815786928079501275771_<136>] SUBMIT/RESERVE

Status

Expression:	(38·10²⁰¹-11)/9
Composite Factor:	472677428675184295354476409692457298375451368493046033188678 587658085293132596953945779446073581537851383760810085981578 6928079501275771 (136-digit)
Status:	Not factored. Not reserved. You can submit its factors or reserve it for submitting in the future.

How to factor it

ECM, P-1, P+1

Look for prime factors by GMP-ECM first. Refer to the section "Efforts by ECM". Not only ECM but also P-1/P+1 may be helpful.

GNFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 203.48-digit and the GNFS difficulty is 135.67-digit. GNFS must be faster than SNFS. It will take about 12 CPU-days to factor this composite number on 64-bit Opteron-2600MHz.

Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 42221_201.
Put the following polynomial file 42221_201.poly in there too.
And then, run "perl factMsieve.pl 42221_201".

42221_201.poly ^*1

# Murphy_E = 3.364307e-11, selected by Jeff Gilchrist
n: 4726774286751842953544764096924572983754513684930460331886785876580852931325969539457794460735815378513837608100859815786928079501275771
Y0: -152281988716461402508176980
Y1: 1202155280352479
c0: 386404564216549113935179918639929
c1: 21308759121961066070183358345
c2: 43932297194040890242910
c3: -51936067883661895
c4: -69988078449
c5: 57720
skew: 739974.21
type: gnfs
# selected mechanically
rlim: 13900000
alim: 13900000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.6
alambda: 2.6

*1 These parameters were not fully adjusted. The approximate expressions which were used for making the parameters are: d=log10(n); time=10^(d/21-4)[hours]; rlim=round(3*10^(d/37+3)); lpbr=floor(d/18+21); mfbr=floor(d/5+28); rlambda=floor(d/26+21)/10;

Efforts by ECM

The efforts by ECM to find small factors of this 136-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 40-digit or more. Please report your efforts by ECM. (Anonymous reports are not acceptable)

Level	B1	Reported runs Total / Required runs (Required runs for lower level)	Name
40	3e6	2336	Wataru Sakai	Apr 20, 2009
40	3e6	2336 / 2336
45	11e6	0 / 3962
45	11e6	/ 3962
50	43e6	0 / 7465 (1130)
50	43e6	/ 7465 (1130)
55	11e7	0 / 17751 (3097)
55	11e7	/ 17751 (3097)
60	26e7	0 / 42014 (7636)
60	26e7	/ 42014 (7636)

Command line to find prime factors up to about 45-digit

echo 4726774286751842953544764096924572983754513684930460331886785876580852931325969539457794460735815378513837608100859815786928079501275771 | ecm -n -c 3962 11e6

Command line to find prime factors up to about 50-digit

echo 4726774286751842953544764096924572983754513684930460331886785876580852931325969539457794460735815378513837608100859815786928079501275771 | ecm -n -c 7465 43e6

Command line to find prime factors up to about 55-digit

echo 4726774286751842953544764096924572983754513684930460331886785876580852931325969539457794460735815378513837608100859815786928079501275771 | ecm -n -c 17751 11e7

Command line to find prime factors up to about 60-digit

echo 4726774286751842953544764096924572983754513684930460331886785876580852931325969539457794460735815378513837608100859815786928079501275771 | ecm -n -c 42014 26e7

Contribution and Reservation

Status

How to factor it

ECM, P-1, P+1

GNFS

See also

Efforts by ECM

Submit polynomial for GNFS

Submit factors

Make reservation