Contribution and Reservation

(38·10¹⁹⁰+7)/9 =: 4(2)₁₈₉3_<191>; = 43 · 7333 · 13729 · 784577 · 122563393 · 1711737271_<10> · 8147524289_<10> · 171022100654158469_<18> · [42524643977349224589225134891943913456977326645461121919072984651236354752610612658812388918557624962658409500393734821499720238963_<131>] SUBMIT/RESERVE

Status

Expression:	(38·10¹⁹⁰+7)/9
Composite Factor:	425246439773492245892251348919439134569773266454611219190729 846512363547526106126588123889185576249626584095003937348214 99720238963 (131-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 191.58-digit and the GNFS difficulty is 130.63-digit. GNFS must be faster than SNFS. It will take about 7 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 42223_190.
Put the following polynomial file 42223_190.poly in there too.
And then, run "perl factMsieve.pl 42223_190".

42223_190.poly ^*1

# Murphy_E = 6.428813e-11, selected by Jeff Gilchrist
n: 42524643977349224589225134891943913456977326645461121919072984651236354752610612658812388918557624962658409500393734821499720238963
Y0: -16190832240823114621644785
Y1: 313765477465793
c0: 125490559162631200018297884052656
c1: 2440600836575047514429479768
c2: -1726795866658892253752
c3: -62146842803229002
c4: 18797252737
c5: 38220
skew: 448486.33
type: gnfs
# selected mechanically
rlim: 10200000
alim: 10200000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
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 131-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 42524643977349224589225134891943913456977326645461121919072984651236354752610612658812388918557624962658409500393734821499720238963 | ecm -n -c 3962 11e6

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

echo 42524643977349224589225134891943913456977326645461121919072984651236354752610612658812388918557624962658409500393734821499720238963 | ecm -n -c 7465 43e6

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

echo 42524643977349224589225134891943913456977326645461121919072984651236354752610612658812388918557624962658409500393734821499720238963 | ecm -n -c 17751 11e7

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

echo 42524643977349224589225134891943913456977326645461121919072984651236354752610612658812388918557624962658409500393734821499720238963 | 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