Contribution and Reservation

4·10²³⁹+1 =: 4(0)₂₃₈1_<240>; = 7 · 47 · 41893 · 1098613 · 520512077 · [50751290197039174977112551431903899323929494349499256480302322628695135287849225834912975184531171005394421043505550569260012632282440159555947336687305498898507812826687595415993327189298091583773830362544443830680533_<218>] SUBMIT/RESERVE

Status

Expression:	4·10²³⁹+1
Composite Factor:	507512901970391749771125514319038993239294943494992564803023 226286951352878492258349129751845311710053944210435055505692 600126322824401595559473366873054988985078128266875954159933 27189298091583773830362544443830680533 (218-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.

SNFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 240.30-digit and the GNFS difficulty is 217.71-digit. SNFS must be faster than GNFS. It will take about 426 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 40001_239.
Put the following polynomial file 40001_239.poly in there too.
And then, run "perl factMsieve.pl 40001_239".

40001_239.poly ^*1

n: 50751290197039174977112551431903899323929494349499256480302322628695135287849225834912975184531171005394421043505550569260012632282440159555947336687305498898507812826687595415993327189298091583773830362544443830680533
m: 10000000000000000000000000000000000000000
deg: 6
c6: 2
c0: 5
skew: 1.16
type: snfs
lss: 1
rlim: 71000000
alim: 71000000
lpbr: 30
lpba: 30
mfbr: 61
mfba: 61
rlambda: 2.7
alambda: 2.7

*1 These parameters were not fully adjusted. The approximate expressions which were used for making the parameters are: deg=expt<=105?4:expt<=210?5:6 or expt<=144?4:6; d=log10(c[deg])+deg*log10(m)[digits]; time=10^(d/30-4)[hours]; skew=|c0/c[deg]|^(1/deg); rlim=round(7*10^(d/60+3)); lpbr=floor(d/25+21); mfbr=floor(d/8+31); rlambda=floor(d/25+18)/10;

Efforts by ECM

The efforts by ECM to find small factors of this 218-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	2111	Wataru Sakai	Feb 21, 2009
40	3e6	2111 / 2111
45	11e6	0 / 3974
45	11e6	/ 3974
50	43e6	0 / 7469 (1133)
50	43e6	/ 7469 (1133)
55	11e7	0 / 17752 (3098)
55	11e7	/ 17752 (3098)
60	26e7	0 / 42014 (7636)
60	26e7	/ 42014 (7636)

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

echo 50751290197039174977112551431903899323929494349499256480302322628695135287849225834912975184531171005394421043505550569260012632282440159555947336687305498898507812826687595415993327189298091583773830362544443830680533 | ecm -n -c 3974 11e6

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

echo 50751290197039174977112551431903899323929494349499256480302322628695135287849225834912975184531171005394421043505550569260012632282440159555947336687305498898507812826687595415993327189298091583773830362544443830680533 | ecm -n -c 7469 43e6

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

echo 50751290197039174977112551431903899323929494349499256480302322628695135287849225834912975184531171005394421043505550569260012632282440159555947336687305498898507812826687595415993327189298091583773830362544443830680533 | ecm -n -c 17752 11e7

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

echo 50751290197039174977112551431903899323929494349499256480302322628695135287849225834912975184531171005394421043505550569260012632282440159555947336687305498898507812826687595415993327189298091583773830362544443830680533 | ecm -n -c 42014 26e7

Submit factors

Make reservation

Back to Factorizations of near-repdigit numbers