Contribution and Reservation

(10¹⁸⁶+11)/3 =: (3)₁₈₅7_<186>; = 4931 · 73081788083755769363_<20> · 119082595147331902970137026564983_<33> · [7767589884898905584453846627616528735466833665717627569798152437068183984890392285268361811654098469581336926528022496076374393063_<130>] (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=3868127526 for P33 / Nov 14, 2008) SUBMIT/RESERVE

Status

Expression:	(10¹⁸⁶+11)/3
Composite Factor:	776758988489890558445384662761652873546683366571762756979815 243706818398489039228526836181165409846958133692652802249607 6374393063 (130-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 186.00-digit and the GNFS difficulty is 129.89-digit. GNFS may be faster than SNFS. It will take about 6 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 33337_186.
Put the following polynomial file 33337_186.poly in there too.
And then, run "perl factMsieve.pl 33337_186".

33337_186.poly ^*1

# Murphy_E = 8.842317e-11, selected by Jeff Gilchrist
n: 7767589884898905584453846627616528735466833665717627569798152437068183984890392285268361811654098469581336926528022496076374393063
Y0: -11183530832595308673377401
Y1: 230100975435947
c0: -15012227132820421940452127255760
c1: 188321184253210442574398186
c2: 317785477333542359855
c3: -7367473982946268
c4: 42833896212
c5: 44400
skew: 243862.11
type: gnfs
# selected mechanically
rlim: 9700000
alim: 9700000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5

*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 130-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 45-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
45	11e6	100	20022002	Mar 22, 2009
		3166	Wataru Sakai	Apr 25, 2009
		3266 / 2972
50	43e6	100	20022002	Mar 22, 2009
		84	Andreas Tete	May 7, 2009
		184 / 6557
		/ 6373
55	11e7	100	20022002	Mar 22, 2009
		100 / 17495 (2744)
		/ 17395 (2644)
60	26e7	0 / 41906 (7482)
60	26e7	/ 41906 (7482)
65	85e7	0 / 69386 (13575)
65	85e7	/ 69386 (13575)

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

echo 7767589884898905584453846627616528735466833665717627569798152437068183984890392285268361811654098469581336926528022496076374393063 | ecm -n -c 6373 43e6

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

echo 7767589884898905584453846627616528735466833665717627569798152437068183984890392285268361811654098469581336926528022496076374393063 | ecm -n -c 17395 11e7

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

echo 7767589884898905584453846627616528735466833665717627569798152437068183984890392285268361811654098469581336926528022496076374393063 | ecm -n -c 41906 26e7

Command line to find prime factors up to about 65-digit

echo 7767589884898905584453846627616528735466833665717627569798152437068183984890392285268361811654098469581336926528022496076374393063 | ecm -n -c 69386 85e7

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