Contribution and Reservation

(34·10²⁰³+11)/9 =: 3(7)₂₀₂9_<204>; = 127 · 4157 · 1084987 · 1576097849_<10> · 267522701219_<12> · 241852534709016633483041799377417_<33> · [6467458742747490908426758718543314878516214661999799045633580159444730768422463131124826108330789481076500407954611602955238945601019157889_<139>] (Serge Batalov / GMP-ECM 6.2.1 B1=1000000, sigma=1984248884 for P33 / Dec 3, 2008) SUBMIT/RESERVE

Status

Expression:	(34·10²⁰³+11)/9
Composite Factor:	646745874274749090842675871854331487851621466199979904563358 015944473076842246313112482610833078948107650040795461160295 5238945601019157889 (139-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 205.93-digit and the GNFS difficulty is 138.81-digit. GNFS must be faster than SNFS. It will take about 17 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 37779_203.
Put the following polynomial file 37779_203.poly in there too.
And then, run "perl factMsieve.pl 37779_203".

37779_203.poly ^*1

# Murphy_E = 2.47882e-11, selected by Jeff Gilchrist
n: 6467458742747490908426758718543314878516214661999799045633580159444730768422463131124826108330789481076500407954611602955238945601019157889
Y0: -547704007448629049153036393
Y1: 3876095718751219
c0: 120962641837821114052609863091200
c1: -2239140492639842857809526700
c2: -44732134564940123623624
c3: 60787651256756811
c4: 172508127714
c5: 131220
skew: 363298.7
type: gnfs
# selected mechanically
rlim: 16900000
alim: 16900000
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 139-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	500	Erik Branger	Mar 21, 2009
		1836	Wataru Sakai	Jul 26, 2009
		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 6467458742747490908426758718543314878516214661999799045633580159444730768422463131124826108330789481076500407954611602955238945601019157889 | ecm -n -c 3962 11e6

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

echo 6467458742747490908426758718543314878516214661999799045633580159444730768422463131124826108330789481076500407954611602955238945601019157889 | ecm -n -c 7465 43e6

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

echo 6467458742747490908426758718543314878516214661999799045633580159444730768422463131124826108330789481076500407954611602955238945601019157889 | ecm -n -c 17751 11e7

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

echo 6467458742747490908426758718543314878516214661999799045633580159444730768422463131124826108330789481076500407954611602955238945601019157889 | 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