Contribution and Reservation

(64·10²¹²+53)/9 =: 7(1)₂₁₁7_<213>; = 3² · 239 · 176243 · 105216983 · 666837176146033_<15> · 851635039121239297_<18> · 873438057987990208763620783_<27> · [35941309491910758486662005234170872074893268643464833137800626414965143974644419293674986363592824138844110998188385283669370273713419521_<137>] SUBMIT/RESERVE

Status

Expression:	(64·10²¹²+53)/9
Composite Factor:	359413094919107584866620052341708720748932686434648331378006 264149651439746444192936749863635928241388441109981883852836 69370273713419521 (137-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 213.81-digit and the GNFS difficulty is 136.56-digit. GNFS must be faster than SNFS. It will take about 13 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 71117_212.
Put the following polynomial file 71117_212.poly in there too.
And then, run "perl factMsieve.pl 71117_212".

71117_212.poly ^*1

# Murphy_E = 3.007195e-11, selected by Jeff Gilchrist
n: 35941309491910758486662005234170872074893268643464833137800626414965143974644419293674986363592824138844110998188385283669370273713419521
Y0: -211663160984019246134837064
Y1: 1616096447972347
c0: -44806407060763673224817170609302133
c1: 426582626917578881784687144441
c2: -6592438073149852871477
c3: -1939352288454424881
c4: -72821073750
c5: 84600
skew: 1300325.84
type: gnfs
# selected mechanically
rlim: 14700000
alim: 14700000
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 137-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	0 / 0
45	11e6	0 / 1022
45	11e6	/ 1022
50	43e6	974	Serge Batalov	Jan 16, 2009
		974 / 7548 (1266)
		/ 6574 (292)
55	11e7	0 / 17421 (2727)
55	11e7	/ 17421 (2727)
60	26e7	0 / 41903 (7494)
60	26e7	/ 41903 (7494)

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

echo 35941309491910758486662005234170872074893268643464833137800626414965143974644419293674986363592824138844110998188385283669370273713419521 | ecm -n -c 1022 11e6

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

echo 35941309491910758486662005234170872074893268643464833137800626414965143974644419293674986363592824138844110998188385283669370273713419521 | ecm -n -c 6574 43e6

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

echo 35941309491910758486662005234170872074893268643464833137800626414965143974644419293674986363592824138844110998188385283669370273713419521 | ecm -n -c 17421 11e7

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

echo 35941309491910758486662005234170872074893268643464833137800626414965143974644419293674986363592824138844110998188385283669370273713419521 | ecm -n -c 41903 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