Contribution and Reservation

(55·10¹⁷⁹-1)/9 =: 6(1)₁₇₉_<180>; = 257 · 557 · 319137174641993_<15> · 7708332067909169_<16> · 34796113231315008583_<20> · [49872749867154635849498114267428018156814293490498079556170309821649579977580220644939911309877042053396719752191315137937549_<125>] SUBMIT/RESERVE

Status

Expression:	(55·10¹⁷⁹-1)/9
Composite Factor:	498727498671546358494981142674280181568142934904980795561703 098216495799775802206449399113098770420533967197521913151379 37549 (125-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 181.04-digit and the GNFS difficulty is 124.70-digit. GNFS must be faster than SNFS. It will take about 4 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 61111_179.
Put the following polynomial file 61111_179.poly in there too.
And then, run "perl factMsieve.pl 61111_179".

61111_179.poly ^*1

# Murphy_E = 1.511136e-10, selected by Jeff Gilchrist
n: 49872749867154635849498114267428018156814293490498079556170309821649579977580220644939911309877042053396719752191315137937549
Y0: -1262649721005303179818433
Y1: 40014062364289
c0: 43183058930049140574416809411680
c1: 878512329756059772155302064
c2: 1595054720124349656554
c3: -16409682066558075
c4: -2410289638
c5: 15540
skew: 437630.99
type: gnfs
# selected mechanically
rlim: 7000000
alim: 7000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
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 125-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 35-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
35	1e6	0 / 0
40	3e6	500	Erik Branger	Mar 7, 2009
		500 / 2337
		/ 1837
45	11e6	0 / 4368 (533)
45	11e6	/ 4368 (533)
50	43e6	0 / 7534 (1246)
50	43e6	/ 7534 (1246)
55	11e7	0 / 17766 (3126)
55	11e7	/ 17766 (3126)

Command line to find prime factors up to about 40-digit

echo 49872749867154635849498114267428018156814293490498079556170309821649579977580220644939911309877042053396719752191315137937549 | ecm -n -c 1837 3e6

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

echo 49872749867154635849498114267428018156814293490498079556170309821649579977580220644939911309877042053396719752191315137937549 | ecm -n -c 4368 11e6

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

echo 49872749867154635849498114267428018156814293490498079556170309821649579977580220644939911309877042053396719752191315137937549 | ecm -n -c 7534 43e6

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

echo 49872749867154635849498114267428018156814293490498079556170309821649579977580220644939911309877042053396719752191315137937549 | ecm -n -c 17766 11e7

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