Contribution and Reservation

(44·10¹⁸⁴-17)/9 =: 4(8)₁₈₃7_<185>; = 19² · 31 · 1779871 · 80370079 · 736415067202097951_<18> · 550975502692803321857_<21> · [75266789839158504125018623404233585934461835467836203551740981194544411644447503788851365320051073591760081253276485126323761439_<128>] SUBMIT/RESERVE

Status

Expression:	(44·10¹⁸⁴-17)/9
Composite Factor:	752667898391585041250186234042335859344618354678362035517409 811945444116444475037888513653200510735917600812532764851263 23761439 (128-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 186.34-digit and the GNFS difficulty is 127.88-digit. GNFS must be faster than SNFS. It will take about 5 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 48887_184.
Put the following polynomial file 48887_184.poly in there too.
And then, run "perl factMsieve.pl 48887_184".

48887_184.poly ^*1

# Murphy_E = 1.015966e-10, selected by Jeff Gilchrist
n: 75266789839158504125018623404233585934461835467836203551740981194544411644447503788851365320051073591760081253276485126323761439
Y0: -4913565367541598957065259
Y1: 88087830362987
c0: 6046443097012199677447535412100
c1: 361702499625691194934744340
c2: -821650778313609498607
c3: -11453505482976008
c4: -19096139676
c5: 26280
skew: 306320.02
type: gnfs
# selected mechanically
rlim: 8600000
alim: 8600000
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 128-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	118	Makoto Kamada	Feb 27, 2009
35	1e6	118 / 0
40	3e6	500	Erik Branger	Mar 17, 2009
		500 / 2318
		/ 1818
45	11e6	0 / 4365 (527)
45	11e6	/ 4365 (527)
50	43e6	0 / 7534 (1244)
50	43e6	/ 7534 (1244)
55	11e7	0 / 17765 (3125)
55	11e7	/ 17765 (3125)

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

echo 75266789839158504125018623404233585934461835467836203551740981194544411644447503788851365320051073591760081253276485126323761439 | ecm -n -c 1818 3e6

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

echo 75266789839158504125018623404233585934461835467836203551740981194544411644447503788851365320051073591760081253276485126323761439 | ecm -n -c 4365 11e6

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

echo 75266789839158504125018623404233585934461835467836203551740981194544411644447503788851365320051073591760081253276485126323761439 | ecm -n -c 7534 43e6

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

echo 75266789839158504125018623404233585934461835467836203551740981194544411644447503788851365320051073591760081253276485126323761439 | ecm -n -c 17765 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